Why Did We Shift from Electron Orbitals to Electron Clouds?

[alan.b]

Atom orbitals, I mean the ones where electrons orbit proton with continuous trajectory like planets orbit around the sun. I do not mean to disagree with modern teachings nor to speculate, I simply do not see how QM actually excludes this possibility. I just want someone walk me through several most convincing experiments and show me how did humanity itself changed their opinion from "electron orbitals" to "electron clouds". I know there are couple of explanations like "electrons would radiate and spiral down to nucleus", but I do not know of any experimental evidence to support that. Also, I was wondering, are there some fields in physics that still use this or similar model of atom based on classical mechanics?

 

[f95toli]

I know there are couple of explanations like "electrons would radiate and spiral down to nucleus", but I do not know of any experimental evidence to support that.

This is how synchrotrons work. They are basically rings where electrons are accelerated in circular orbits which in turn makes the electrons radiate light.

So there is actually a field of technology which is based upon the fact that orbiting electrons loose energy...

 

[SpectraCat]

Atom orbitals, I mean the ones where electrons orbit proton with continuous trajectory like planets orbit around the sun. I do not mean to disagree with modern teachings nor to speculate, I simply do not see how QM actually excludes this possibility. I just want someone walk me through several most convincing experiments and show me how did humanity itself changed their opinion from "electron orbitals" to "electron clouds". I know there are couple of explanations like "electrons would radiate and spiral down to nucleus", but I do not know of any experimental evidence to support that. Also, I was wondering, are there some fields in physics that still use this or similar model of atom based on classical mechanics?

An electron in a classical orbit would have a non-zero angular momentum. However, the angular momentum of the H-atom ground state has been measured to have an angular momentum of exactly zero, in accordance with the "cloud-like" version of atomic orbitals predicted by quantum mechanics.

 

[alan.b]

This is how synchrotrons work. They are basically rings where electrons are accelerated in circular orbits which in turn makes the electrons radiate light.

So there is actually a field of technology which is based upon the fact that orbiting electrons loose energy...

Ok, thank you.

- why electrons in QM not radiate, or do they?

- how does synchrotron read electron radiation?

- what kind of radiation electrons emit, how often?

- is it not electron the most elementary amount of electric charge, so how can the smallest amount of something, that has no size, radiate anything and what would be left of a single electron if it radiates even a single photon?

 

[alan.b]

An electron in a classical orbit would have a non-zero angular momentum. However, the angular momentum of the H-atom ground state has been measured to have an angular momentum of exactly zero, in accordance with the "cloud-like" version of atomic orbitals predicted by quantum mechanics.

I suppose all the solar system planets, moons, binary stars or whatever classical mechanics systems have this non-zero angular momentum? Can you say where does this non-zero angular momentum come from? How does QM predict zero angular momentum? Thank you.

 

[SpectraCat]

I suppose all the solar system planets, moons, binary stars or whatever classical mechanics systems have this non-zero angular momentum? Can you say where does this non-zero angular momentum come from? How does QM predict zero angular momentum? Thank you.

The fact that you are asking these questions indicates to me that I cannot answer them in a way that you can appreciate. I would suggest that you read up on some basic physics and reconsider your questions.

I will just say now that angular momentum *is* the cross product of a particle's position and momentum vectors. In qualitative terms, since there is always curvature of the particle's (or planet's) trajectory in the orbiting systems you mention, then the cross product above must always be non-zero. Where angular momentum "comes from" is a much deeper question that I cannot really answer.

The QM prediction of zero angular momentum for the H-atom ground state arises from the perfect spherical symmetry of the probability distribution describing the ground state atomic orbital.

 

[jfy4]

The radiation of photons from an electron is the direct result of an equation, which says that accelerating charges radiate. The formula looks something like this for low velocities.

P=Kq^{2}a^{2}

where P is the power radiated and a is the acceleration, q is the charge, and K is just a lot of constants together.

The type of radiation is electromagnetic radiation, or light.

The radiation of light from an accelerating charge, must come from the particles kinetic energy... so a dimensionless particle, that we both can agree can have momentum, loses it kinetic energy to radiation.

These next words, I am not sure how much they'll resonate but here i go...
Solutions for the hydrogen atom using the time independent Schrodinger equation give us energy eigenstates which are stationary. Only specific situations where evolution in time is a concern matters when it comes to a particle radiating.

i hope this helps a little...

 

[varga]

It's me, Alan. Major meltdown here, moving to a new address, I broke my laptop, changing internet provider... in short, I have no idea what was my password and I can't retrieve it via my old e-mail, so I got my flatmate to open this account.

The fact that you are asking these questions indicates to me that I cannot answer them in a way that you can appreciate. I would suggest that you read up on some basic physics and reconsider your questions.

I will just say now that angular momentum *is* the cross product of a particle's position and momentum vectors. In qualitative terms, since there is always curvature of the particle's (or planet's) trajectory in the orbiting systems you mention, then the cross product above must always be non-zero. Where angular momentum "comes from" is a much deeper question that I cannot really answer.

Ok, I had no idea what momentum you were talking about, was it individual, combined and what relation did it have to what point of reference. I see now that by "angular momentum" you simply mean 'non-linear' or 'curved trajectory'. Out of curiosity, if something was moving left-right in a straight line, making 180 degree turns, what would be its angular momentum?

The QM prediction of zero angular momentum for the H-atom ground state arises from the perfect spherical symmetry of the probability distribution describing the ground state atomic orbital.

What symmetry has to do with angular momentum?

How was this angular momentum measured for the H-atom?

Do planetary orbits not have symmetrical probability distribution?

 

[varga]

The radiation of photons from an electron is the direct result of an equation, which says that accelerating charges radiate. The formula looks something like this for low velocities.

P=Kq^{2}a^{2}

where P is the power radiated and a is the acceleration, q is the charge, and K is just a lot of constants together.

The type of radiation is electromagnetic radiation, or light.

Thank you, but is this radiation actually directly measured in any experiment or is it only indirectly derived? I understand electrons slow down in particle accelerators, but this is not actual measurement of radiation.


Would it be unreasonable to suppose electrons in orbit around the nucleus do not accelerate as much as assumed, but rather follow some "curvature of space-time" and really traversing rather straight line from their point of view and their reference frame?

The radiation of light from an accelerating charge, must come from the particles kinetic energy... so a dimensionless particle, that we both can agree can have momentum, loses it kinetic energy to radiation.

These next words, I am not sure how much they'll resonate but here i go...
Solutions for the hydrogen atom using the time independent Schrodinger equation give us energy eigenstates which are stationary. Only specific situations where evolution in time is a concern matters when it comes to a particle radiating.

i hope this helps a little...

I see what you are saying, exchange of potential and kinetic energy - lift a ball up from the ground and you will give it potential energy, let it go and as it falls down it losses potential energy and gains kinetic energy in a form of velocity, thus the energy is conserved. So, where does radiation come into this, again?

Do planets radiate, and if so why do planets not spiral into the Sun?



There is only ONE explanation why would electrons in QM atom model not radiate:

- they appear at one location and reappear at another location(s), but the sequence of these points do not connect with a continuous line, it's not a trajectory you could draw without lifting a pen from a paper (the time when electron is nowhere), rather its trajectory is a collection of unconnected dots. Is this how it is supposed to be according to QM?

 

[jfy4]

For your first part yes, you can measure that radiation for sure. eject electrons into a uniform magnetic field at right angles to each other and you will have electrons going in a circle radiating a lot, just make sure they have a large centripetal acceleration ;)

You seem to have misunderstood my last part about radiation, which is my fault for not being clear, i will try harder here.

As an electron is accelerated, it radiates energy. That energy has to be something. For charges, the energy comes from the kinetic energy of the charge, so the charge slows down.

Planets do radiate, although its a little silly to talk about it because it is undetectable. only large sources produce gravitational radiation profound enough for us to detect. The radiation from orbiting planets is almost nothing, and so does extremely little to affect orbit.

i hope this is clearer... and helps

 

[f95toli]

Thank you, but is this radiation actually directly measured in any experiment or is it only indirectly derived? I understand electrons slow down in particle accelerators, but this is not actual measurement of radiation.

There are a number of huge synchrotron facilities around the world where they generate X-Rays using this technique, many modern measurement techniques in materials science, biotech etc are based on radiation emitted from accelerating electrons. The "hard" X-rays generated in synchrotron are ideal for e.g. determining the structure of proteins etc.

Here is a link to one such facility
http://www.maxlab.lu.se/

 

[Frame Dragger]

There are a number of huge synchrotron facilities around the world where they generate X-Rays using this technique, many modern measurement techniques in materials science, biotech etc are based on radiation emitted from accelerating electrons. The "hard" X-rays generated in synchrotron are ideal for e.g. determining the structure of proteins etc.

Here is a link to one such facility
http://www.maxlab.lu.se/

I would just add that you can SEE synchroton light. Here, it's a bit Čerenkov-ish http://upload.wikimedia.org/wikipedia/commons/4/4a/Synchrotron_radiation.jpg

 

[varga]

For your first part yes, you can measure that radiation for sure. eject electrons into a uniform magnetic field at right angles to each other and you will have electrons going in a circle radiating a lot, just make sure they have a large centripetal acceleration ;)

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

Like that? However, the radiation there is due to electrons colliding with gas molecules in the bulb. Show me the same thing in vacuum and you will convince me.

... energy has to be something. For charges, the energy comes from the kinetic energy of the charge, so the charge slows down.

Yes, energy of charges (electrons) comes from their mass and its velocity too, but primarily from their electromagnetic potentials. The energy stored in electromagnetic fields does not degrade over time or due to any interaction, just like energy stored in gravitational potential is constant in relation to its mass, and herein lies the problem.


Let's take a proton to be our model of Earth and let's take an electron to represent the Moon, and let's imagine these are the only two particle in the universe. Let's put this electron "above" the proton, let's measure the energy of our system at this initial position where both are stationary, and now let us turn our simulation on, let the electron "free fall" towards the proton.

As it gets closer it will accelerate and exchange field potential energy to gain this velocity, just as free falling objects in gravity field. The closer it gets the more it accelerates, but then you say it also radiates more, or does it absorb photons in this case? So, what happens when this electron gets really close and is supposed to have the greatest velocity, does it actually slow down? If it did slow down, then Coulomb's law would be seriously flawed, however it seem to work just fine, just as well as Newton's law of gravitation. And, if we started with only two particles, how many photons did they manage to emit, how many particles are there now, and how is the energy conserved?

Now, let us shift this electron to one side a bit just enough so they miss each other. As the electron flies by and moves away it is supposed to decelerate according to Coulomb's law, but you say it is also supposed to radiate, or again, perhaps absorb photons in this case, but what is there to absorb if nothing else is anywhere near?

I hope we are not talking about "virtual photons".

Planets do radiate, although its a little silly to talk about it because it is undetectable. only large sources produce gravitational radiation profound enough for us to detect. The radiation from orbiting planets is almost nothing, and so does extremely little to affect orbit.

Let's calculate some real numbers, let's take the number of electrons in Earth and plug it in that formula, take acceleration from Earth spin, rotation around Sun and rotation of solar system around galaxy, what is the P equal to?

If that's nothing, than perhaps it's nothing for electrons in atom orbit too. Has anyone tried to plug in some real numbers and see what would be the speed, radius, acceleration and radiation of an electron in classical orbit around a proton?

 

[Frame Dragger]

I love that photograph of the electron beam circling in the gas... so lovely.

 

[PhaseShifter]

Let's take a proton to be our model of Earth and let's take an electron to represent the Moon, and let's imagine these are the only two particle in the universe. Let's put this electron "above" the proton, let's measure the energy of our system at this initial position where both are stationary, and now let us turn our simulation on, let the electron "free fall" towards the proton.

Let's start here and make one small change--give the electron just enough sideways momentum that the attraction of the proton should pull it into a circular orbit.

This model is essentially a rotating dipole, which will produce an oscillating electric field. These oscillations will radiate through space, carrying energy away from the location of the electron-proton system. In a classical system, this means the electron must be losing an equal amount of energy, and the orbit must therefore degrade towards one with a lower potential.

Now the electron is circling the proton even faster, and therefore emitting higher frequency radiation. This means it loses energy faster and faster until the radius of the orbit is zero.

This would be an infinite change in potential, which obviously doesn't happen with real atoms.

 

[SpectraCat]

Show me the same thing in vacuum and you will convince me.

Try googling "free-electron laser" ... those generate stimulated emission of radiation due to the controlled acceleration of electrons in (for example) a periodically-poled magnetic field.

Has anyone tried to plug in some real numbers and see what would be the speed, radius, acceleration and radiation of an electron in classical orbit around a proton?

Yes, in the early 1900's. Try googling "Bohr atomic model" for the details.

Or check here: http://en.wikipedia.org/wiki/Atomic_theory#First_steps_towards_a_quantum_physical_model_of_the_atom

and here: http://en.wikipedia.org/wiki/Larmor_formula

 

[jfy4]

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

Like that? However, the radiation there is due to electrons colliding with gas molecules in the bulb. Show me the same thing in vacuum and you will convince me.




Yes, energy of charges (electrons) comes from their mass and its velocity too, but primarily from their electromagnetic potentials. The energy stored in electromagnetic fields does not degrade over time or due to any interaction, just like energy stored in gravitational potential is constant in relation to its mass, and herein lies the problem.


Let's take a proton to be our model of Earth and let's take an electron to represent the Moon, and let's imagine these are the only two particle in the universe. Let's put this electron "above" the proton, let's measure the energy of our system at this initial position where both are stationary, and now let us turn our simulation on, let the electron "free fall" towards the proton.

As it gets closer it will accelerate and exchange field potential energy to gain this velocity, just as free falling objects in gravity field. The closer it gets the more it accelerates, but then you say it also radiates more, or does it absorb photons in this case? So, what happens when this electron gets really close and is supposed to have the greatest velocity, does it actually slow down? If it did slow down, then Coulomb's law would be seriously flawed, however it seem to work just fine, just as well as Newton's law of gravitation. And, if we started with only two particles, how many photons did they manage to emit, how many particles are there now, and how is the energy conserved?

Now, let us shift this electron to one side a bit just enough so they miss each other. As the electron flies by and moves away it is supposed to decelerate according to Coulomb's law, but you say it is also supposed to radiate, or again, perhaps absorb photons in this case, but what is there to absorb if nothing else is anywhere near?

I hope we are not talking about "virtual photons".





Let's calculate some real numbers, let's take the number of electrons in Earth and plug it in that formula, take acceleration from Earth spin, rotation around Sun and rotation of solar system around galaxy, what is the P equal to?

If that's nothing, than perhaps it's nothing for electrons in atom orbit too. Has anyone tried to plug in some real numbers and see what would be the speed, radius, acceleration and radiation of an electron in classical orbit around a proton?

Im still not understanding your issue with the radiation reaction force... Why can an electron not lose kinetic energy to radiation? In fact, they way i see it, you said the correct thing which compliments what i said before. The energy of the charge cannot come from its potential, that leaves really one other source for losing energy, from kinetic. The radiation from a charge come at the expense of its kinetic energy.

Conservation of energy comes about because the energy lost by the electron is the energy radiated. Is that clear? I am not sure how else to explain this... I really hope this is making sense.

For gravitational radiation, I am not going to do the calculation for you, because i believe it. I believe it because many experimentalist are, as we speak, working to detect gravitational radiations from sources, and hence, have worked out the math them selves, hoping to match prediction with observation. however, i will give you the formula and you can do it becuase you are the skeptical one ;)

\frac{dE}{dt}=\frac{1}{5}\frac{G}{c^{5}}\left<\dddot{I}_{ij}\dddot{I}^{ij}}\right>

with

I^{ij}= \mathcal{I}^{ij}-\frac{1}{3}\delta^{ij}I^{k}_{k}

with

\mathcal{I}^{ij}=\int d^{3}x \mu x^{i}x^{j}

where \mu is the mass density

I hope this helps clear some things up.

 

[varga]

@Frame Dragger

Thanks, if it weren't for you I would never realize this is actually called "synchrotron radiation", even if that was kind of the 1st thing f95toli said, and even your phrasing "synchrotron light" did not directly lead me to this realization.


http://en.wikipedia.org/wiki/Synchrotron_radiation
- "...immediately signaled to turn off the synchrotron as "he saw an arc in the tube." The vacuum was still excellent..."

Ok, I admit these people are smart since their first suspicion was the same as mine, hehe - that something is wrong with the vacuum. If that photo of yours shows radiation that is in vacuum and not due to any collisions, then I'm convinced there is some weird radiation there, I'll call it "synchrotron radiation" and I will accept all the equations of this theory.

 

[varga]

Let's start here and make one small change--give the electron just enough sideways momentum that the attraction of the proton should pull it into a circular orbit.

This model is essentially a rotating dipole, which will produce an oscillating electric field.

We have two smallest amounts of electric charge there can be, these two electric fields can not create any more electric fields, because the field energy is constant, and discrete. I agree these two fields, including all the magnetic fields that go along, will oscillate (orbit) around, the question is for how long.

These oscillations will radiate through space, carrying energy away from the location of the electron-proton system. In a classical system, this means the electron must be losing an equal amount of energy, and the orbit must therefore degrade towards one with a lower potential.

Now the electron is circling the proton even faster, and therefore emitting higher frequency radiation. This means it loses energy faster and faster until the radius of the orbit is zero.

Ok, let's say they do radiate and lose energy, so how long it would take for it to spiral down - million years, ten minutes, a second? In any case, how do you describe electron motion of QM atom model, how is it possible for them to not radiate, how can they move in a certain area without acceleration, without making any corners? How can they move without making curved trajectories like in bubble chambers and that photo of pink electron beam?

 

[varga]

Try googling "free-electron laser" ... those generate stimulated emission of radiation due to the controlled acceleration of electrons in (for example) a periodically-poled magnetic field.

Ok, I'm now very familiar with with these accelerators but I'm still suspicious whether there is any collision going on there, because I could not find a picture where it is obvious electrons are not colliding like the one I posted where electrons in gas go circles.

Yes, in the early 1900's. Try googling "Bohr atomic model" for the details.

Or check here: http://en.wikipedia.org/wiki/Atomic_theory#First_steps_towards_a_quantum_physical_model_of_the_atom

and here: http://en.wikipedia.org/wiki/Larmor_formula

Ok, but I'm not sure if they actually modeled the interaction by integrating Coulomb's law and practically solving a two-body problem by numerical integration and modeling motion with Newton's laws of motion and kinematics equations, or did they use some more statistical equations with sin/cos, harmonics, spring-like oscillations or something like that?

But wait the second, that theory ignores this radiation for the most part, except when electron jumps orbits, it is actually still working and applicable model as I understand.

 

[PhilDSP]

I hope we are not talking about "virtual photons".

What's wrong with virtual photons? They're an ingenious, almost legitimate way to begin to model and understand sub-quantum levels of near-field radiation and energy (from within a framework that does not allow you to do that)

 

[varga]

Im still not understanding your issue with the radiation reaction force... Why can an electron not lose kinetic energy to radiation? In fact, they way i see it, you said the correct thing which compliments what i said before. The energy of the charge cannot come from its potential, that leaves really one other source for losing energy, from kinetic. The radiation from a charge come at the expense of its kinetic energy.

Ok, we're getting close. I agree with that, but before I answer your question let me just boil it down a little bit more. If electron's mass is to stay constant, then the "change in kinetic energy" can only mean "change in velocity".

Conclusion:
- The radiation (if any) from a charge can only come at the expense of its VELOCITY.


Your question:
- Why electron should not lose kinetic energy to radiation?

http://en.wikipedia.org/wiki/Potential_energy
* Potential energy is energy stored within a physical system as a result of the position or configuration of the different parts of that system. It has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process.

* According to the principle of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy.


http://en.wikipedia.org/wiki/Electric_potential_energy
* Electric potential energy aka "electrostatic potential energy" is a potential energy associated with the conservative Coulomb forces within a defined system of point charges.


http://en.wikipedia.org/wiki/Electronvolt
* By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt.


Conclusion:
- The definition of the most basic unit of energy, 'electron volt', would not work.

Conservation of energy comes about because the energy lost by the electron is the energy radiated. Is that clear? I am not sure how else to explain this... I really hope this is making sense.

It is clear, but not possible according to classical physics and electrodynamics.


My questions:
- ELECTRON VOLT EXPERIMENT: Let's put an electron two volts of potential difference "above" the nucleus, let's measure the energy of our system at this initial position where both are stationary, and now let us turn our simulation on - let the electron "free fall".

As it gets closer it accelerates and exchanges its potential energy for kinetic energy, its position for velocity. After some time it completely passes through electric potential difference of one volt. Now, tell us what is its velocity (kinetic energy) at this point? When do electrons radiate (or absorb), when they slow down or speed up?

 

[f95toli]

It is clear, but not possible according to classical physics and electrodynamics.

Of course it is possible. Synchrotron radiation is fairly easy to explain once you take into account relativistic effects; this has been know for about a hundred years (which is why people knew that the "orbit model" could not be correct even back then) and has nothing to do with with quantum mechanics. Most of chapter 14 of Jackson (which is THE book on classical electrodynamics) deals with radiation by moving charges (and sections 14.5-14.7 deals with synchrotron radiation).

Also, remember that we are talking about charges traveling at relativistic speeds, the normal expressions for kinetic energy etc are not applicable.

 

[PhilDSP]

As it gets closer it accelerates and exchanges its potential energy for kinetic energy, its position for velocity. After some time it completely passes through electric potential difference of one volt. Now, tell us what is its velocity (kinetic energy) at this point? When do electrons radiate (or absorb), when they slow down or speed up?

An electron (attached to an atom) loses energy to the photon when it radiates. So it drops down to a lower energy state which is closer to the nucleus. In doing so it must travel more quickly around the nucleus to balance the attraction of the nucleus so its velocity increases.

When absorbing radiation, the electron gains energy and so jumps further from the nucleus and reduces its velocity.

But those are the passive effects (not the cause of radiation according to the Bohr model).

I think the apparent contradiction in terms of kinetic energy gain or loss is that linear momentum is exchanged for angular momentum and vice versa.

 

[jfy4]

Ok, we're getting close. I agree with that, but before I answer your question let me just boil it down a little bit more. If electron's mass is to stay constant, then the "change in kinetic energy" can only mean "change in velocity".

Conclusion:
- The radiation (if any) from a charge can only come at the expense of its VELOCITY.


Your question:
- Why electron should not lose kinetic energy to radiation?

http://en.wikipedia.org/wiki/Potential_energy
* Potential energy is energy stored within a physical system as a result of the position or configuration of the different parts of that system. It has the potential to be converted into other forms of energy, such as kinetic energy, and to do work in the process.

* According to the principle of conservation of energy, energy cannot be created or destroyed; hence this energy cannot disappear. Instead, it is stored as potential energy.


http://en.wikipedia.org/wiki/Electric_potential_energy
* Electric potential energy aka "electrostatic potential energy" is a potential energy associated with the conservative Coulomb forces within a defined system of point charges.


http://en.wikipedia.org/wiki/Electronvolt
* By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt.


Conclusion:
- The definition of the most basic unit of energy, 'electron volt', would not work.





It is clear, but not possible according to classical physics and electrodynamics.


My questions:
- ELECTRON VOLT EXPERIMENT: Let's put an electron two volts of potential difference "above" the nucleus, let's measure the energy of our system at this initial position where both are stationary, and now let us turn our simulation on - let the electron "free fall".

As it gets closer it accelerates and exchanges its potential energy for kinetic energy, its position for velocity. After some time it completely passes through electric potential difference of one volt. Now, tell us what is its velocity (kinetic energy) at this point? When do electrons radiate (or absorb), when they slow down or speed up?

Sorry about the order of this,

Your progress through, and conclusion to your middle argument about the functionality of an electron volt is unorganized, and I am unable to follow it at all, would you mind making your argument more explicit. The conclusion seems to have nothing to do with the content cited before hand, save the last, which defined an electron volt accurately.

The first part of your post talked about the radiation reaction and it seems you accept now that a charges radiation is at its kinetic energy's expense. I am not sure what else you are talking about after this part. if we both agree that a particle's speed reduces because of the radiation reaction, then what seems to be the problem? You do understand that a particle can be subject to multiple forces correct? It can both be accelerated, arbitrarily forward and backwards, if you will, and still have a net acceleration in one direction.

The energy radiated has nothing to do with the particle's potential energy which, as you stated, is a function of position alone, but its kinetic energy which is radiated away in the form of photons, thus slowing the particle down.

yes potential energy can be converted to kinetic, and kinetic energy is radiated away by the charge, causing the charge to accelerate less.

Is that clear?

Im really at wits end here, especially because you seem to be almost saying the same thing i am, but somehow interpreting as a violation of the conservation of energy or some bad definition of an electron volt...

all the energy of the system is still there, not destroyed or created, but in a different form.

Please be more clear if you can :)

 

[varga]

Im really at wits end here, especially because you seem to be almost saying the same thing i am, but somehow interpreting as a violation of the conservation of energy or some bad definition of an electron volt...

all the energy of the system is still there, not destroyed or created, but in a different form.

Please be more clear if you can :)

I think it's very clear and that you should respond more directly to citations from Wikipedia. For example, what part of "conservative Coulomb forces" is not clear to you?

Can you please at least answer my question directly so I can make my point and respond to the rest of your message without making anyone repeat themselves. ELECTRON VOLT EXPERIMENT: Let's put an electron two volts of potential difference "above" the proton and measure the energy of the system at this initial position where both are stationary, then let the electron "free fall". After some time it passes through electric potential difference of one volt, at this point, what is its velocity and kinetic energy?

 

[varga]

Of course it is possible. Synchrotron radiation is fairly easy to explain once you take into account relativistic effects; this has been know for about a hundred years (which is why people knew that the "orbit model" could not be correct even back then) and has nothing to do with with quantum mechanics. Most of chapter 14 of Jackson (which is THE book on classical electrodynamics) deals with radiation by moving charges (and sections 14.5-14.7 deals with synchrotron radiation).

Also, remember that we are talking about charges traveling at relativistic speeds, the normal expressions for kinetic energy etc are not applicable.

I did not count relativistic effects as a part of classical physics and electrodynamics.

I'm pretty sure bubble chamber trajectories need no any relativistic corrections to be accurately predicted, classical Coulomb and Lorentz forces in combination with kinematics equation (Newton's laws of motion) will do the job. But I do not really know what effects are you talking about, I don't have that book, can you throw some keywords so I can look into it at Wikipedia? I know about relativistic equations for kinetic energy, I do not think any of that is part of the definition for 'electron volt'.

 

[SpectraCat]

I think it's very clear and that you should respond more directly to citations from Wikipedia. For example, what part of "conservative Coulomb forces" is not clear to you?

Can you please at least answer my question directly so I can make my point and respond to the rest of your message without making anyone repeat themselves. ELECTRON VOLT EXPERIMENT: Let's put an electron two volts of potential difference "above" the proton and measure the energy of the system at this initial position where both are stationary, then let the electron "free fall". After some time it passes through electric potential difference of one volt, at this point, what is its velocity and kinetic energy?

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

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

By the way, don't worry about the definition of an electron volt .. it is not phenomenologically defined, as you seem to be assuming. It is simply a collection of fundamental constants corresponding to the *ideal* case from your quote. An actual free-electron cannot be accelerating, because then it isn't free, it is interacting with a potential.

 

[PhaseShifter]

I think it's very clear and that you should respond more directly to citations from Wikipedia. For example, what part of "conservative Coulomb forces" is not clear to you?

What part of electrodynamics is missing in your description? hint: Your picture of the electric field is incomplete.

 

[jfy4]

I think it's very clear and that you should respond more directly to citations from Wikipedia. For example, what part of "conservative Coulomb forces" is not clear to you?

Can you please at least answer my question directly so I can make my point and respond to the rest of your message without making anyone repeat themselves. ELECTRON VOLT EXPERIMENT: Let's put an electron two volts of potential difference "above" the proton and measure the energy of the system at this initial position where both are stationary, then let the electron "free fall". After some time it passes through electric potential difference of one volt, at this point, what is its velocity and kinetic energy?

The part that is unclear to me is what the conservative coulomb force has to do with conservation of energy violations, and the problem with the definition of an electron volt...

Spectra cat has just answered your electron volt experiment, which we already knew, trivially, because we knew the definition of an electron volt... and you must have been able to get the velocity from that.

It is unclear to me what is even the problem you are addressing... please write it out so i can help, I am really trying to.

 

[varga]

An electron (attached to an atom) loses energy to the photon when it radiates. So it drops down to a lower energy state which is closer to the nucleus. In doing so it must travel more quickly around the nucleus to balance the attraction of the nucleus so its velocity increases.

When absorbing radiation, the electron gains energy and so jumps further from the nucleus and reduces its velocity.

But those are the passive effects (not the cause of radiation according to the Bohr model).

I think the apparent contradiction in terms of kinetic energy gain or loss is that linear momentum is exchanged for angular momentum and vice versa.

Yes, I think the contradiction is apparent too. I see more than one:


1.) Electron slows down when it radiates photons...

- it's velocity (trajectory) would jerk at specific interval, because the energy packets have a certain minim and are discrete - quantified. we do not observe this sudden jerks in electron trajectories, I believe.

- does it slow down BECAUSE it radiates a photon, or it radiates because it slows down?

- if electron in orbit has the constant velocity, is its "acceleration" due to 'change in direction' actually 'acceleration' or 'deceleration' and is it suppose to radiate, absorb, or both in this case?


2.) Electron slows down when it radiates photons, so it drops down to a lower energy state which is closer to the nucleus.

- closer to nucleus may be "lower energy" state in terms of the whole system and principle of the least resistance, but the *actual energy* of the electron (and the whole system) should stay the same and is compensated by increased velocity, there is no room for radiation here.

- put proton and electron 1mm apart where electron has energy Ep=A, move electron to 2mm distance where Ep=B, now move the electron with acceleration or with constant velocity from point A to point B, note that energy of the system and electron energy must not change due to any derivative of the position separately, but strictly according to the relation with the distance, i.e. position itself.


3.) Electron slows down when it radiates photons, drops down to a lower energy state, in doing so its velocity increases.

- which one, slows down or speeds up? causality, i do not see logical sequence there, is it all happening simultaneously?

- if its velocity actually increases at the end, does that not mean it absorbed a photon?

- again, is acceleration causing radiation or is absorption of radiation causing acceleration?

 

[PhaseShifter]

3.) Electron slows down when it radiates photons, drops down to a lower energy state, in doing so its velocity increases.

- which one, slows down or speeds up? causality, i do not see logical sequence there, is it all happening simultaneously?

- if its velocity actually increases at the end, does that not mean it absorbed a photon?

- again, is acceleration causing radiation or is absorption of radiation causing acceleration?

Emitting the photon and dropping to a lower energy state are simultaneous. There is no "slowing down".

Although, to be more technical a wave packet that resembles an orbiting electron is actually a superposition of many states rather than a single state, and would actually merely be changing the relative amplitudes of component wavefunctions.

 

[PhilDSP]

Emitting the photon and dropping to a lower energy state are simultaneous. There is no "slowing down".

Since the ejection of the photon is going to be outward from the center of the atom, the photon's momentum will be away from the center. The reactive change of the electron's momentum will correspondingly be inward forcing the drop to the lower energy state.

Although, to be more technical a wave packet that resembles an orbiting electron is actually a superposition of many states rather than a single state, and would actually merely be changing the relative amplitudes of component wavefunctions.

Yes, we should point out that we're working with the Bohr model which we know to be a caricature of the real situation.

 

[varga]

Your progress through, and conclusion to your middle argument about the functionality of an electron volt is unorganized, and I am unable to follow it at all, would you mind making your argument more explicit.

I expected you would know about potential energy. I'll address that in relation to my example of electron volt experiment. Meanwhile, I'd like you to say something about these three explicit and specific questions:

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

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

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

if we both agree that a particle's speed reduces because of the radiation reaction, then what seems to be the problem?

The energy radiated has nothing to do with the particle's potential energy which, as you stated, is a function of position alone, but its kinetic energy which is radiated away in the form of photons, thus slowing the particle down.

yes potential energy can be converted to kinetic, and kinetic energy is radiated away by the charge, causing the charge to accelerate less.

Is that clear?

No, it's slightly funny.


F= k* m1m2/r2 or F= k* q1q2/r2 -> acceleration= F/m

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?

 

[PhaseShifter]

Yes, we should point out that we're working with the Bohr model which we know to be a caricature of the real situation.

Yes, this is where his question is a little confusing--orbiting packets aren't eigenfunctions of the Hamiltonian operator, and thus don't have a well-defined energy. But a classical system with orbiting particles doesn't have quantized energy states, and the electrons would spiral into the nucleus as they continuously radiated EM waves into the surroundings.

Historically the Bohr model is important for first explaining the various series of lines in atomic spectra. The mathematics indicated quantized energy states for the bound electron, but the model itself couldn't explain why angular momentum had to be quantized, and that's why it was replaced after just a decade.

I sometimes suspect that the only reason it's still taught is that people have problems visualizing an electron as a complex wavefunction rather than a particle with well-defined position and momentum.

Even now most textbooks don't attempt to explain that the odd-shaped orbitals with multiple lobes are actually superpositions of wavefunctions with opposite angular momentum, so the imaginary part of the complex numbers conveniently cancels out.

 

[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.