Why does decoherence not fully solve the measurement problem?

[Frame Dragger]

I'm not trying to take a swipe, I'm just kind of blunt. As for the physics, I think the main issue with your argument is: electron in potential well -> lower well = needing a HIGHER energy state in the silver, not a lower one as you described when you laid it all out on the last page.

As for why it wouldn't spontaneously act, there is always the possiblity that the electron will tunnel. The other issue I have is what SpectraCat has mentione: this seems to be a scenario in which no image could develop, just "static". I know that you're saying this is an advanced application for a partial theory (and I respect that), but it seems to be a large hole. The energy issue first and foremost however...

Btw, thanks for giving me the best answer you have (unfinished personal processes are just that after all) as to your interpretation. It helps me understand where you're coming from, and I'm willing to look at QM from any angle as long as I can return to instrumentalism.

 

[conway]

I'd like to respond but you haven't quite made it clear to me whether you are willing to discuss this question in terms of the simplified potential well model that I proposed or whether you are going to insist that I deal with the full-blown chemistry of silver bormide.

 

[Frame Dragger]

I'd like to respond but you haven't quite made it clear to me whether you are willing to discuss this question in terms of the simplified potential well model that I proposed or whether you are going to insist that I deal with the full-blown chemistry of silver bormide.

Oh, now that I see what you're getting at, yes please explain what you feel comfortable with. I don't say that I'll agree, but I won't be looking at you as though you've gone cross-eyed either.

So, my issue with your potential well model is that your "step" involves a higher energy state devolving, which makes sense. What doesn't make sense, is why that doesn't occur as a result of a photon's energy being "dumped" into the system. I understand that we're not talking about photographic plate here, but a model; go for it, I'd like to hear.

 

[conway]

So, my issue with your potential well model is that your "step" involves a higher energy state devolving, which makes sense.

I'm honestly having trouble parsing this sentence: if it makes sense, why do you have an issue with it?

What doesn't make sense, is why that doesn't occur as a result of a photon's energy being "dumped" into the system. I understand that we're not talking about photographic plate here, but a model; go for it, I'd like to hear.

OK, here's how it goes.

If we can think about the potential wells for the time being, this is the case I want to analyze. There is one electron and there are three states: electron in well A (source), electron in well B (target), and electron in the “condcution band” (C). The system starts off with the electron in state A.

According to the traditional picture, when a photon is incident on the system, there is a probability the electron will go from A to C. Once it is in C, there is a probability that it drop back down either to A (where it started) or to B. Once it drops into B it is trapped, whether B is at a higher or lower potential than A. (I know so far this is just a model, but for the sake of reference, that’s your speck of silver.)

I’m working a different picture. I allow the system to be driven by an oscillating electric field that couples A and C. After a time we may find the electron in a superposition of 90% A and 10% C. Since C and B are also coupled, the wave function may evolve further so that the electron finds itself in a superposition of 90% A, 10% C and 1% B. (Due to rounding, percentages may not add to exactly 100.)

The next step is where I haven’t yet been able to fill in the details. If you can help me out here I am willing to share the Nobel Prize with you. I turn off the electric field and watch what happens. What I am looking for is a mechanism whereby the electron can drain out of A into B via C. You can call it “quantum siphoning”.

There is plenty of energy available to drive the process, just as there is in an ordinary siphon. The problem is that when C couples to B, it is true that the probability drains from C to B which is what we want. And energy is released which we would like to use in order to replenish C from A, to keep the process moving. Just like an ordinary siphon. The probelm is that the energy at B is released in the form of radiating electromagnetic energy, and it is not clear to me how I recapture it with good efficiency at A, especially if A is relatively far from B. And I absolutely need to recapture it, because remember I've turned off the electric field.

That’s my problem. Perhaps you will agree that the solution I’m looking for is vaguely transactional in Cramer’s sense. There might be other ways of making it work but I haven’t figure it out yet.

 

[Frame Dragger]

Hmmm... It sounds like a mixture of the TI and quantum tunneling in reverse. I'll be honest, I need time to think about this. I understand the traditional picture well enough, but... without an incident photon to drive the reaction, what's to keep the superpositions from evolving in a radically different way so that there is no connection between the "oscillating field" and the behaviour of the electron?

Still, just keeping to the problem you've raised, I have no CLUE how you could recpature whatever is released at B, unless you posit that somehow the coupling of A and C initially sets the stage for a complete return of the energy emitted at B. I'm not an expert, but... that seems impossible. Really... really impossible. In fact, the idea of doing what you propose is a bit like finding a 100% efficient blanket for a fusion plant (to produce Tritium) to capture neutrons... you can't afford a miss.

Of course, if the well's themselves could have some kind of entangled state that is as yet unsuspected...

Hm... I don't think I should spend my share of the nobel cash. ;)

 

[zonde]

The next step is where I haven’t yet been able to fill in the details. If you can help me out here I am willing to share the Nobel Prize with you.

I am quite willing to participate in discussion that is interesting for me without any promise of Nobel Prize. But entirely different matter would be if you will be about to invent hyperdrive and would be promising to share a trip to Alpha Centauri.

I turn off the electric field and watch what happens. What I am looking for is a mechanism whereby the electron can drain out of A into B via C. You can call it “quantum siphoning”.

There is plenty of energy available to drive the process, just as there is in an ordinary siphon. The problem is that when C couples to B, it is true that the probability drains from C to B which is what we want. And energy is released which we would like to use in order to replenish C from A, to keep the process moving. Just like an ordinary siphon. The probelm is that the energy at B is released in the form of radiating electromagnetic energy, and it is not clear to me how I recapture it with good efficiency at A, especially if A is relatively far from B. And I absolutely need to recapture it, because remember I've turned off the electric field.

Let's assume that medium for waves has nonlinear properties so that ordinary wave becomes very sensitive to small perturbations and is unstable. However soliton waves are quite stable.
In that case there can be situation that is quite reversed from not being able to recapture energy to situation where it is quite hard to get rid of energy when the radiation can not form soliton wave.

Maybe simpler way to look at that is to assume two electron and one positron superposition. Positron should not escape somewhere very fast so it is quite reasonable that it can be recaptured annihilating one of the electrons.

 

[conway]

I'm glad you're enjoying the discussion but although I have to confess I don't know what solitons are, I think you're probably off target by invoking them in this instance.

The interaction between the free and bound waves of a potential well is fairly unambiguous and straightforward in the Schroedinger representation, and it is nothing more exotic than ordinary electromagnetic radiation. You can see this most easily by inspecting a superposition of the first and second bound states of the well, and watching how the probability shifts back and forth from left to right with the passage of time. It's exactly equivalent to a small classical antenna and in fact the rate of energy loss is given by the classical antenna formulas.

The waves in question when dealing with the free states are not all that different, and the radiation is still governed by antenna equations. This is the energy that is dissipated when the free state evolves into the bound state, and this is the energy that we I have spoken about wanting to recapture.

 

[SpectraCat]

Hi conway,

I still don't have a lot of time to spend on PF right now, but I just wanted to give a brief comment on your latest model. One issue that I see with it is that you are modeling the initial transition that drives the electron into the conduction band as if it were between discrete states. In fact it is not, the electron starts out in the valence band and is promoted to the conduction band upon photon absorption. These bands are comprised of very closely spaced quantum levels that very nearly approximate a local continuum of states. Therefore, I don't think you can use the simple model you have proposed for understanding the coupling of the photon. I am not really that strong with band-theory, but if you just look at the spectra width of these bands, which are quite broad with respect to discrete molecular bands, you will find that the lifetimes are very short ... I expect that they are too short to allow the kind of coherent state preparation you are trying to set up, because of decoherence.

So, the electron will stay in the conduction band ... but it very quickly evolve into a superposition of states that doesn't have much spectral overlap with the "hole" it left behind (which is also a broad superposition), so the probability of stimulating the reverse transition is very low. You might be able to look up some information on this if you search "stimulated electron-hole recombination". I will check it myself later, but I have to get back to work.

 

[conway]

But my model is simply a three state system; there's no decoherence or anything like that going on. We can argue about how well my model reflects the photographic process, but I thought we were going to suspend that argument for the time being.

If I can explain the collapse of the wavefunction even within my simplified model, I think it would be worth something. We can then turn to the photographic process and see how it impacts on that question. We're just not there yet.

 

[Frame Dragger]

Hmmm... I'm going to research "Stimulated electron-hole recombination" and see if that helps to illuminate the subject, thanks SpectraCat.

@Conway: True, but maybe the reason you're stuck is that there is no model which allows the recapture you're looking for... at least, not that can be used to model the photographic process. If your model can never be expanded to describe physical procesess, then I fail to see the value in explaining collapse within such restrictions if they are known to be non-physical.

EDIT: I know that we're going back to the photographic process here, but I think this is interesting. http://arxiv.org/ftp/physics/papers/0405/0405035.pdf I don't believe it can help you, but it is... well... it's worth the read.

 

[conway]

@Conway: ...maybe the reason you're stuck is that there is no model which allows the recapture you're looking for... at least, not that can be used to model the photographic process. If your model can never be expanded to describe physical procesess, then I fail to see the value in explaining collapse within such restrictions if they are known to be non-physical.

If that's the way you feel I guess I'm going to have to withdraw my offer to share the Nobel Prize money with you. Anyhow, I don't exactly need your help anymore because I think I figured it out. But it was nice at least for a while to not be treated as a total crank, if only for a couple of days.

 

[conway]

Maybe I was a little hasty when I said I didn't need to share my Nobel Prize money with you guys. What happened is I figured out how to make my Quantum Siphoning work. You can't do it with just two potential wells; you need millions of them, which is what you actually have in a crystal. I wrote it all up on my blogsite (you can find it if you just google "Quantum Siphoning"). But I'm having a little snag getting anyone to seriously look at my paper. I submitted it to the American Journal of Physics and it was rejected within 48 hours (!). And I don't have the endorsement needed to put it up on arXiv.org. So it looks like I could use a co-author to help me out here.

 

[yoda jedi]

Why does decoherence not fully solve the measurement problem? I know that must have been discussed here before a lot, maybe someone can me direct to a earlier thread or post that explains it well?

I read some QM texts, but they mostly do not discuss decoherence. I know something with 'definite outcomes' and 'eigenspace selection' troubles the decoherence approach, but never understood what it means...

thank you

it can be solved by a nonlinear quantum mechanics (SQM not, and without MWI).

I think it does solve it in the context of a many-worlds interpretation that doesn't throw away the Born rule (i.e. not the Everett version), but I don't know if anyone has ever really spelled out all the details.

You will probably find the discussion in Schlosshauer's book enlightening.

Also note that there is no "measurement problem" in the ensemble interpretation. The problem only exists for people who believe that QM describes reality, even at times between state preparation and measurement.

I probably won't try to elaborate much on these things, because I have found that discussions about interpretations are very time consuming, and I'm kind of busy with other things right now.

RIGHT !
clever insight

called ψ-complete view, unlike ψ-epistemic.
as for ψ-epistemic which quantum states are solely representative of our knowledge.

 

[cesiumfrog]

only a literal handful of silver atoms

(I don't think that word means what you think it means.)

Let a photon pass through a pinhole so it spreads out. When it hits a photographic plate, it is absorbed. It is absorbed over the whole surface of the plate and ceases to exist. It does not resolve itself into a "position eigenstate of the photon". At the same time, a silver halide crystal undergoes an irreversible phase transition. That doesn't mean the photon got concentrated at the location of the crystal. The crystal didn't need the entire energy of the photon undergo a change of state

Conway, your idea was basically that the energy of the photon is spread over the entire surface that it is shone at, and that localised detection doesn't actually prove the entire photon to have become localised again?

Lets say we have a single detector with a large input-area, that registers once for each time a photon is shone at it. Now let's move the detector twice as far away from the source, and replace this single detector with a panel of four independent detectors (each identical to the first).

According to standard physics, each time we trigger a photon emission, exactly one of the detectors will respond.

According to your "interpretation", each time: there is a 42% chance of exactly one detector responding, a 32% chance of none responding, 21% chance of two both responding to the same photon, nearly a 5% chance of the photon being detected in three different places, and 0.4% chance that all the detectors respond to the photon.

Do you stand by this?

 

[cesiumfrog]

What about an electron going through the Stern Gerlach apparatus? It divides into two beams: that is it's "state". When it hits the detector screen the two streams jointly excite a single bound wave function within the screen; at the same time, a crystal on the surface changes state. How do we know that the newly-excited bound wave function doesn't have the same spin that the electron had BEFORE entering the SG apparatus? There is no need to think that the electron, originally in a composition of two spin states, has resolved itself into one state or the other simply because a particular crystal in one branch of the wave stream has changed color.

What about if one of the two beams is directed through a second Stern Gerlach apparatus, why shouldn't you then expect a total of three beams?

 

[conway]

(I don't think that word means what you think it means.)


Conway, your idea was basically that the energy of the photon is spread over the entire surface that it is shone at, and that localised detection doesn't actually prove the entire photon to have become localised again?

Lets say we have a single detector with a large input-area, that registers once for each time a photon is shone at it. Now let's move the detector twice as far away from the source, and replace this single detector with a panel of four independent detectors (each identical to the first).

According to standard physics, each time we trigger a photon emission, exactly one of the detectors will respond.

According to your "interpretation", each time: there is a 42% chance of exactly one detector responding, a 32% chance of none responding, 21% chance of two both responding to the same photon, nearly a 5% chance of the photon being detected in three different places, and 0.4% chance that all the detectors respond to the photon.

Do you stand by this?

I made a mistake when I said "let a photon pass through a pinhole". It wasn't exactly a mistake because I never like to use the word photon, but I thought for the sake of brevity I could get away with it in context. I should have said "let an amount of electromagnetic energy on the order of a single photon pass through a pinhole". I didn't mean to imply that it's possible to shoot a single photon just like you'd shoot a pea through a straw.

I know there are people who claim to do magical things with single photon sources, but I don't know much about these things. I suspect it's harder to do than you think; in particular, I doubt that the experiment you've described has been carried out in exactly the way you describe it, although I've heard there are related experiments which claim to show the thing that you're driving at.

I do know something about more traditional light sources, like thermal sources and lasers. Laser soursces are easiest to analyze because the photon statistics are Poisson. If you can possibly frame your objections to my "interpretation" in terms of laser or thermal light I might be able to deal with them.

 

[collinsmark]

Hello conway,

I've been following this thread with great interest. But I have some questions.

I made a mistake when I said "let a photon pass through a pinhole". It wasn't exactly a mistake because I never like to use the word photon, but I thought for the sake of brevity I could get away with it in context. I should have said "let an amount of electromagnetic energy on the order of a single photon pass through a pinhole". I didn't mean to imply that it's possible to shoot a single photon just like you'd shoot a pea through a straw.

It almost sounds like you are saying that when measured, photons do not behave as containing discrete packets of energy. Can your model handle the experimental evidence involving the photoelectric effect?

In other words, could your model distinguish between a laser shining through a small hole with a given frequency and intensity (intensity at the photographic paper) and a different laser at half the frequency with twice the intensity (maybe intensity isn't the right word here. Perhaps "twice the number of photons" might be better)? (Assume the experiment is set up such that the hole size and laser intensities are such that the same diffraction pattern is produced, and the overall electromagnetic power hitting the paper is the same in both cases -- only the frequency is different).

According to your model, since the energy is evenly distributed across the photographic paper, and since the energy is equal in both cases, how would your model predict/explain the different behavior between the two cases confirmed by experimental evidence (photoelectric effect)?

I know there are people who claim to do magical things with single photon sources, but I don't know much about these things. I suspect it's harder to do than you think; in particular, I doubt that the experiment you've described has been carried out in exactly the way you describe it, although I've heard there are related experiments which claim to show the thing that you're driving at.I do know something about more traditional light sources, like thermal sources and lasers. Laser soursces are easiest to analyze because the photon statistics are Poisson. If you can possibly frame your objections to my "interpretation" in terms of laser or thermal light I might be able to deal with them.

What if the photon source is swapped with an electron beam shooting through a crystal lattice. Electrons are subject to diffraction and interference too (such as in the electron version of the double-slit experiment). And as we know, electrons can expose photographic paper too.

According to your model, would the energy of an electron also be spread across paper (via its spread out wave function)? What about its charge? Is the charge localized when measured, or is it spread out too? Perhaps a more pertinent question is looking at it in terms of cesiumfrog's request, with the 4 identical detectors at twice the distance. In this configuration, would your model predict that if a single electron is ejected from the source, that there is a chance that multiple electrons could be detected?

 

[conway]

I don't really have a theory other than the idea of combining Schroedinger's equation and Maxwell's equations. It's surprising how many things you can explain with just this combination without worrying about things like "photons". In theory this should be pretty mainstream but it doesn't seem to be all that widespread. Even at the highest levels it seems you find people who aren't familiar with some of the basic pictures. For example, if you write the Schroedinger equation for the hydrogen atom and take a superposition of the s and p states, you get a tiny classical antenna. Everything the hydrogen atom does electromagnetically can pretty much be explained in terms of the properties of this antenna. You ask me if my theory can explain this or that...so for starters, I have to ask you if you recognize this picture of the hydrogen atom?

 

[collinsmark]

Hello conway,

I'm not sure I follow you here.

I am familiar with the the energy eigenstates of an electron in a hydrogen atom, and the concept of superposition of states. If I had to, I could dust off my old Griffiths book or something and calculate up the wave-function equations for an electron being in a superposition of an s and p state (such as \Psi = \frac{1}{\sqrt{2}}|(n=1, l=0, m_l=0, s= 1/2)> \ + \ \frac{1}{\sqrt{2}}|(2, 1, 0, 1/2)>, or whatever energy eigenstates are chosen). But conceptually, I can imagine the results. If the wave-function is in a superposition of two energy eigenstates, the expectation value and phase will oscillate back and forth in some way, which might resemble a rotation, or it might resemble simple harmonic motion (in some ways), or perhaps a time-varying bimodal distribution like two pistons in an engine, depending on which energy eigenstates are part of the superposition.

I've also studied radio frequency communications theory, and I'll give you that there are surprising similarities in the mathematics between it and QM, with all the Fourier transforms, Bessel functions, and the like.

But I don't get the connection to the antenna. Even though the wave-function's expectation value may be varying with time due to the superposition of states, the atom is not radiating electromagnetic energy due to this. If it was, QM would have serious conservation of energy problems. If left completely isolated, hydrogen atoms would widdle away to nothing (assuming that it stayed in the superposition of states indefinitely [i.e same thing as saying no photons were released or absorbed]). So I think I can recognize the picture of an electron's wavefunction in a superposition of energy eigenstates in a hydrogen atom, but no, I don't see how that relates to a classical antenna.

[Edit: my knowledge of quantum electrodynamics (above and beyond non-relativistic quantum mechanics) is presently rather sparse, but from what I can gather, I am not presently aware of electrons radiating energy when being in a superposition of states, even though the expectation value of the wave-function may oscillate.]

 

[Frame Dragger]

@collinsmark: My limited understand of QED (which was recently bolstered by researcing it after being roundly spanked here) would indicate that they would oscillate, but not radiate, as you say.

@conway: I don't see how that forms a classical antenna... I think I'd need to see the math or a model. The thing is, if it DID act as an antenna, collinsmark would be right... we'd have a universe of radiation and nothing else because the electron would crash into its hydrogen neuclus.

 

[conway]

Hello conway,


But I don't get the connection to the antenna. Even though the wave-function's expectation value may be varying with time due to the superposition of states, the atom is not radiating electromagnetic energy due to this. If it was, QM would have serious conservation of energy problems. If left completely isolated, hydrogen atoms would widdle away to nothing (assuming that it stayed in the superposition of states indefinitely [i.e same thing as saying no photons were released or absorbed]). So I think I can recognize the picture of an electron's wavefunction in a superposition of energy eigenstates in a hydrogen atom, but no, I don't see how that relates to a classical antenna.

This oscillation of charge is exactly why the atom radiates. Or absorbs, depending on the circumstance (because it might be acting as a receiving antenna). It makes a lot of sense to look at the atom this way:

1. It explains why the eigenstates are stable. They are the only states that don't have oscillating charge distributions.

2. It explains the energy transfer between the electromagnetic field and the atom. If the atom is in the ground state and it is driven at the difference frequency between the ground and the excitied states, it will oscillate at that frequency, putting it in a superposition of those two states. As an absorbing antenna, it continues to draw power from the external field and as it does, the p component grows at the expense of the s component. The more the p component grows the stronger it oscillates, and it soon reaches an equilibrium where the abosrbed energy equals the re-scattered energy.

3. It explains the decay rate (or linewidths) of the atomic spectrum. You can easily calculate the power output of the atom using the classical antenna formulas, and it gives you the correct values.

There is basically nothing that the atoms do in terms of their interaction with the electric field that you can't explain by treating them as little classical antennas.

 

[SpectraCat]

This oscillation of charge is exactly why the atom radiates. Or absorbs, depending on the circumstance (because it might be acting as a receiving antenna). It makes a lot of sense to look at the atom this way:

1. It explains why the eigenstates are stable. They are the only states that don't have oscillating charge distributions.

2. It explains the energy transfer between the electromagnetic field and the atom. If the atom is in the ground state and it is driven at the difference frequency between the ground and the excitied states, it will oscillate at that frequency, putting it in a superposition of those two states. As an absorbing antenna, it continues to draw power from the external field and as it does, the p component grows at the expense of the s component. The more the p component grows the stronger it oscillates, and it soon reaches an equilibrium where the abosrbed energy equals the re-scattered energy.

3. It explains the decay rate (or linewidths) of the atomic spectrum. You can easily calculate the power output of the atom using the classical antenna formulas, and it gives you the correct values.

There is basically nothing that the atoms do in terms of their interaction with the electric field that you can't explain by treating them as little classical antennas.

There is some qualitative insight to be gained from this model, but I wonder if it is really as correct as you seem to be claiming. In particular, when you use a time-dependent perturbation (i.e. a classical electric field) to drive a two-level quantum system (like your atom in the above example), you will observe characteristic Rabi oscillations. These arise from the well defined relationship between the quantum phases of the two states. I can't see how the *qualitative* phenomenon (let alone the quantitative relationship) of Rabi oscillations can be reproduced in your framework.

So, I think I agree that your model may be useful for qualitative understanding of some time-integrated properties of atoms interacting with EM radiation, but I don't think it will properly reproduce the true time-dependent behavior. Also, I'd like to see your derivation for point 3 above ... I find it hard to believe that you can reproduce the Einstein coefficient for spontaneous emission from the Larmor formula for power emission (which I guess is what you are talking about). This is especially true since, as you say, when the atom is in the excited *eigenstate*, there is no oscillating charge in the first place. So perhaps I just don't understand what you are trying to say in point 3 above.

 

[conway]

There is probably nothing more cassical at the atomic level than the Rabi oscillations. It's exactly what a synchronous motor does when it's close to but not exactly running at line frequency: absorbs energy, then regenerates, absorbs, then regenerates, as its phase alternately goes in and out of synch with the line.

And yes, I'm saying the Einstein coefficients all come out of the basic antenna formulas. The one for spontaneous emission is just based on the strength of the antenna when it is in a superposition of the two states, with no external field.

I'm not going to be able to do the exact calculation, but I can sketch it out more or less. You take the length of the dipole as being on the order of 1 angstrom; the wavelength of light is close to 100 A for the s-p transition; this gives you an electric length of 1/100 which gives you a radiation resistance of approx. .01 ohms (there's a formula for this somewhere). You take the current as being one electron every 10^(-16) seconds which is approx. 1 milliamp (10^-3); the power of the antenna is then I-squared-R = 10 nanowatt (10^-8). If I divide the energy of the excited state (0.75 Ry = approx 10^(-18 J)) by the power, then I get a charateristic time of around 100 picoseconds (10^-10).

I don't know that this is very different from Einstein's number.

 

[SpectraCat]

There is probably nothing more cassical at the atomic level than the Rabi oscillations. It's exactly what a synchronous motor does when it's close to but not exactly running at line frequency: absorbs energy, then regenerates, absorbs, then regenerates, as its phase alternately goes in and out of synch with the line.

Yes of course there are driven classical systems that display oscillatory behavior ... what I don't understand is how you get such behavior out of your classical antenna model. It's been a while since I worked through all the classical electrodynamics, so I can't be sure, but it seems to me that (if anything) the two-level atom would be more like a classical crystal resonator than an antenna. Perhaps in that case you can get the Rabi-like behavior, but in a classical antenna there is no characteristic resonance frequency, right? I mean, doesn't a classical antenna absorb in a broadband fashion? (Like I said, I haven't looked at that stuff for a while, so I am not completely sure I am correct in this case.) In any case, I think this a case where the phenomenological model would benefit from some mathematical support.

And yes, I'm saying the Einstein coefficients all come out of the basic antenna formulas. The one for spontaneous emission is just based on the strength of the antenna when it is in a superposition of the two states, with no external field.

Except that spontaneous emission can occur from pure excited eigenstates, which are *not* described by your superposition states. So there is no way to start the classical process you are describing.

I'm not going to be able to do the exact calculation, but I can sketch it out more or less. You take the length of the dipole as being on the order of 1 angstrom; the wavelength of light is close to 100 A for the s-p transition; this gives you an electric length of 1/100 which gives you a radiation resistance of approx. .01 ohms (there's a formula for this somewhere). You take the current as being one electron every 10^(-16) seconds which is approx. 1 milliamp (10^-3); the power of the antenna is then I-squared-R = 10 nanowatt (10^-8). If I divide the energy of the excited state (0.75 Ry = approx 10^(-18 J)) by the power, then I get a charateristic time of around 100 picoseconds (10^-10).

I don't know that this is very different from Einstein's number.

Interesting .. I think you are only off by a little more than an order of magnitude .. the actual lifetime is a bit more than a nanosecond IIRC. I think that this is likely coincidental, since the physics behind your model is not really correct. What you are describing is the characteristic time for the energy to flow out of a classical oscillator, once the process of emission has started. On the other hand, the Einstein A coefficient is related to the probability that the stable excited eigenstate will decay in a certain time interval. This is related to the coupling to the background vacuum fluctuations, and can be derived from first principles using Fermi's Golden Rule in the context of QED. (The original Einstein coefficients were phenomenologically derived). Furthermore, in this framework, the emission process is basically instantaneous (as one would expect since the photon is quantized).

So, like I said, there are some useful qualitative insights to be gained from your picture to be sure, but I think that one must be cautious about attaching too much physical significance to the analogy. Stretching things to far would probably lead to incorrect interpretations/conclusions/predictions, since the underlying physics does not seem to be correct. My guess is it is the latter point that keeps this conceptual picture from being discussed very much in formal classes and textbooks.

 

[conway]

Yes of course there are driven classical systems that display oscillatory behavior ... what I don't understand is how you get such behavior out of your classical antenna model. It's been a while since I worked through all the classical electrodynamics, so I can't be sure, but it seems to me that (if anything) the two-level atom would be more like a classical crystal resonator than an antenna. Perhaps in that case you can get the Rabi-like behavior, but in a classical antenna there is no characteristic resonance frequency, right?

No, this is incorrect. A quarter-wave dipole is rather broadband, but the atomic case corresponds to the very short tuned dipole. I calculated the resonance in my last post. you can get the Q-factor by multiplyting the characteristic time by the frequency. Using my numbers is comes to 10^6. This is also a different way of expressing the linewidth.

Except that spontaneous emission can occur from pure excited eigenstates, which are *not* described by your superposition states. So there is no way to start the classical process you are describing.

Those pure excited eigenstates you talk about are an artifact of your Copenhagen interpretation. In the semiclassical picture you're not responsible for considering these cases, because all your atoms are in a superposition to begin with. In any event, the minute one of your pure states bumps into another atom, it is thrown into a superposition, so the point is moot.

Interesting .. I think you are only off by a little more than an order of magnitude .. the actual lifetime is a bit more than a nanosecond IIRC. I think that this is likely coincidental, since the physics behind your model is not really correct.

I think it's a pretty good coincidence considering I just pulled those numbers out of my ***. But if you want to write it off to beginner's luck, I can't argue with that.

What you are describing is the characteristic time for the energy to flow out of a classical oscillator, once the process of emission has started. On the other hand, the Einstein A coefficient is related to the probability that the stable excited eigenstate will decay in a certain time interval. This is related to the coupling to the background vacuum fluctuations, and can be derived from first principles using Fermi's Golden Rule in the context of QED. (The original Einstein coefficients were phenomenologically derived).

You say it can be derived from first principles, but I have to point out that so far I'm the only one who has used a theory (antenna theory) to come up with some numbers. I'm understanding from the word "phenomenological" that Einstein basically had to get his numbers from experiment.

So, like I said, there are some useful qualitative insights to be gained from your picture to be sure, but I think that one must be cautious about attaching too much physical significance to the analogy. Stretching things to far would probably lead to incorrect interpretations/conclusions/predictions, since the underlying physics does not seem to be correct. My guess is it is the latter point that keeps this conceptual picture from being discussed very much in formal classes and textbooks.

Does this mean you believe in the existence of a benevolent cabal of wise overseers who decide what we should think about and what we shouldn't?

 

[SpectraCat]

No, this is incorrect. A quarter-wave dipole is rather broadband, but the atomic case corresponds to the very short tuned dipole. I calculated the resonance in my last post. you can get the Q-factor by multiplyting the characteristic time by the frequency. Using my numbers is comes to 10^6. This is also a different way of expressing the linewidth.

Ok, I guess I'll have to take your word for that for now. Do you have a derivation of how the Rabi oscillations are reproduced by your model?

Those pure excited eigenstates you talk about are an artifact of your Copenhagen interpretation. In the semiclassical picture you're not responsible for considering these cases, because all your atoms are in a superposition to begin with. In any event, the minute one of your pure states bumps into another atom, it is thrown into a superposition, so the point is moot.

It's not "my CI" .. it is STANDARD QUANTUM MECHANICS! It is "the most successful theory in physics"! Furthermore, regardless of interpretation, any semi-classical picture is only an approximation to the full quantum description. Stable eigenstates are consistent with experimental data, and thus I am on *very* solid ground considering them to be real. They are most certainly *not* an artifact .. that is a very bold claim, unless you have a competing description that shows similar consistency with the broad range of experimental phenomena that have been shown to support SQM.

Atomic collisions are a separate and distinct kind of perturbation which can be fully accounted for in SQM-based descriptions of atomic lineshapes, so that doesn't get you off the hook at all. Spontaneous emission has been observed for H-atoms and other quantum eigenstates in rarefied samples where the mean collision-free lifetime of the atoms exceeds the spontaneous emission lifetime by orders of magnitude. So if your theory can't explain spontaneous emission from eigenstates, then it is has a major flaw.

I think it's a pretty good coincidence considering I just pulled those numbers out of my ***. But if you want to write it off to beginner's luck, I can't argue with that.

As I said, my criticisms are not with your numbers (an order of magnitude is fine for an estimation), but rather with the underlying physical model. I have made clear statements about what I think the flaws are, and you have chosen not to address them. That is your choice, but I think that my statements are close to what you will get from any other expert.

You say it can be derived from first principles, but I have to point out that so far I'm the only one who has used a theory (antenna theory) to come up with some numbers. I'm understanding from the word "phenomenological" that Einstein basically had to get his numbers from experiment.

Why does it always come down to this kind of statement with you? Everything I am referring to is in the well-known mainstream of science ... it is not my own theory, which is why I don't have to do the legwork you seem to want to see. The lifetime of the H-atom 2p->1s transition is well known .. it is around 1.6 ns once you take into account all the relativistic effects .. google it if you want a more precise value. There are also ample websites where the precise formula for the Einstein A-coefficients can be found, so you can plug in the constants for yourself and check the agreement of *your* number.

I don't remember the precise history of the Einstein coefficients, and I couldn't find it online in the short time I had to search, but I believe that Einstein's major contribution was to prove that the probabilities for stimulated emission and absorption had to be related to the probabilities for spontaneous emission according to a simple phenomenological model. I don't know how much they knew about the spontaneous emission lifetime at the time. As far as the current understanding is concerned .. just do a wiki search, and you will see a complete expression for the A coefficient in terms of fundamental constants, and the energy spacing of the coupled levels. As I said, one of the early successes of quantum field theory was the derivation of the correct expressions for the Einstein coefficients from first principles (I think it was done by Dirac). Again, there is no speculation here .. there are well-accepted scientific facts and principles I am citing.

Does this mean you believe in the existence of a benevolent cabal of wise overseers who decide what we should think about and what we shouldn't?

Get real ... it means I think that physics should be as correct as possible almost all of the time. In cases where high-quality theories (i.e. SQM) are available, and the current case is an example, then approximate theories should be used with caution, and you shouldn't be surprised if the experts choose to eschew them in favor of the superior theory. In practice, approximate theories can often be used successfully, but they are most useful when the are based on approximate descriptions of the *correct* physical picture, and the approximations need to be carefully stated, so that it is easy to judge the regimes where the model will start to break down. In rare cases, models based on incorrect physics can persist for some time, take the Bohr model of the atom for example, based on their pedagogic usefulness and historical value.

*That* is the criteria I believe is used to judge what goes in physics textbooks ... not some conspiracy-minded drivel.

 

[DrChinese]

Does this mean you believe in the existence of a benevolent cabal of wise overseers who decide what we should think about and what we shouldn't?

You found out the truth! How did you escape from their mind control?

 

[conway]

It's not "my CI" .. it is STANDARD QUANTUM MECHANICS! It is "the most successful theory in physics"! Furthermore, regardless of interpretation, any semi-classical picture is only an approximation to the full quantum description. Stable eigenstates are consistent with experimental data, and thus I am on *very* solid ground considering them to be real. They are most certainly *not* an artifact .. that is a very bold claim, unless you have a competing description that shows similar consistency with the broad range of experimental phenomena that have been shown to support SQM.

I don't know why you take my use of the phrase "your Copenhagen interpretation" as some kind of provocation. I simply mean to remind you that you and I have different interpretations. In your interpretation, the individual atoms of hydrogen in a heated gas are either in the ground state or one of the excited states, distributed according to temperature. That is what I mean by "your Copenhagen interpretation".

In my semi-classical interpretation it is not that way. Individual hydrogen atoms are in a superposition of states. The total s and p energies are the same in your interpretation and mine, but I have them distributed within individual atoms. That's why my atoms radiate: because they're in a superposition of states. The combination of emission and absorption puts them in equilibrium with the electromagnetic field. My model doesn't have any atoms (or perhaps only a few) in pure eigenstates.

I know this next statement will irritate you, but it must be said nevertheless: I am not aware of any experiment which distinguishes between my model and your model. Yes, I know your model is consistent with the experimental data: my point is, so is mine. You cannot refute my model by saying that it doesn't handle the case of pure eigenstates (and that was after all the only counterargument you raised), because I believe those states are merely an artifact of your model.

 

[Frame Dragger]

I don't know why you take my use of the phrase "your Copenhagen interpretation" as some kind of provocation.

Becuase "Your..." always sounds like "Your PRECIOUS... *sarcasm*" in these contexts. It IS provacative language, hence the use of it in cheesy villain dialogue.

"Where's god now priest?" Sounds bad coming from a little girl puking green.

"Where's your god now priest?" Sounds much worse.

Why?

Still thinking?

Your implies that you utterly disagree with it, and hold it in low regard. You're distancing yourself from it entirely, and not only that, you're giving ownership (that is implied you would not accept for anything) of this theory/interpretation/god/chocolate/etc... of that thing to the person you're adressing. In essence, it is the rhetorical equivalent of shoving a hand-grenade into someone's mouth, and then running like hell.

 

[SpectraCat]

I don't know why you take my use of the phrase "your Copenhagen interpretation" as some kind of provocation. I simply mean to remind you that you and I have different interpretations. In your interpretation, the individual atoms of hydrogen in a heated gas are either in the ground state or one of the excited states, distributed according to temperature. That is what I mean by "your Copenhagen interpretation".

Can you really not see how arrogant and clueless it seems for you to put your own, non-peer reviewed, unverified personal interpretation of Q.M. on the same footing with the standard interpretation that is backed up by 100+ years of solid, peer-reviewed experimental and theoretical literature, and then expect others to do the same? You are free to develop your own interpretation, but you need to recognize that others will not simply take it a face value when it conflicts (or appears to conflict) with the standard interpretation. I would think that you would welcome such criticism, because in order for your model to have any chance to survive, it must be able to withstand such scrutiny.

That is the provocation I draw from your statement ... it is nothing personal. When you use the pronoun "my", you really mean your own personal interpretation, so your use of the pronoun "your" should be symmetrical. I am citing the standard, verified, peer-reviewed version, and that is how you should refer to it. The equivalent, non-provocative version of

In my semi-classical interpretation it is not that way. Individual hydrogen atoms are in a superposition of states.

What physical principles is that model based on? Why are such superposition states more believable to you than eigenstates? You need to provide such a basis for your model to be convincing. The fact is that in the absence of a perturbation, the coefficients for your superposition will be time invariant, so a 90% s-, 10% p-state will stay that way forever (or until perturbed). SQM provides a description of how such superposition states would radiate (the square modulus of the p-coefficient describe the probability of finding the system in the p-state, which can undergo spontaneous emission). How does your model explain it? It seem that it would just predict emission of a classical field with 10% of the energy of the full transition ... that is fine for a classical field, since the energy is proportional to the electric field amplitude ... it's a problem for quantized photons though, since your frequency will have to change.

What I am getting at is that you seem to be just picking and choosing a few parts of QM to include in your model (i.e. discrete atomic levels). That will lead to problems when you need to describe phenomena that are not incorporated in your model. For example, what about the selection rule based on conservation of angular momentum? These are experimentally verified. How does angular momentum appear in your model?

As I have said a couple of times already ... let's see the mathematical framework supporting your model. That will make it much easier to understand the nitty-gritty details.

The total s and p energies are the same in your interpretation and mine, but I have them distributed within individual atoms. That's why my atoms radiate: because they're in a superposition of states. The combination of emission and absorption puts them in equilibrium with the electromagnetic field. My model doesn't have any atoms (or perhaps only a few) in pure eigenstates.

What absorption? What equilibrium? In the absence of an energy source, there is a net flow or energy out of the system in the form of photons. So the spontaneous emission of radiation is inherently a non-equilibrium phenomenon.

Also, you last sentence indicates that the eigenstates *do* exist in your model ... so now you also have to explain why these entities (which apparently are not just artifacts if you use them in your model), behave differently in your interpretation than in SQM.

I know this next statement will irritate you, but it must be said nevertheless: I am not aware of any experiment which distinguishes between my model and your model. Yes, I know your model is consistent with the experimental data: my point is, so is mine. You cannot refute my model by saying that it doesn't handle the case of pure eigenstates (and that was after all the only counterargument you raised), because I believe those states are merely an artifact of your model.

Again with the "your model" nonsense .. please refer to it as "the standard model", so that other observers reading this thread realize the unequal footing these two descriptions are on. You claim your semi-classical model is consistent with the experimental data, but so far you have made a few qualitative arguments and one quantitative estimate that was off by an order of magnitude. I have given you some starting points to close this gap ... Rabi oscillations (quantitative, not qualitative), angular momentum conservation rules ... there are plenty of other fine points like spin-orbit coupling and the Lamb shift waiting in the wings.

Your "belief" about eigenstates being artifacts is frankly irrelevant. The standard interpretation which predicts the existence of eigenstates has been shown to be consistent with a vast array of experimental results going far beyond the couple of examples you have mentioned here. You are free to believe what you like, however, posting on here indicates that you are trying to convince others that your interpretation has some validity. If you want to convince us that eigenstates are artifacts, or even to consider an alternative description that doesn't use them (although yours seems to need them), the you will have to do better than saying "you don't believe in them." You have to show us why some alternative provides a better (unlikely) or clearer (perhaps) description of the observed phenomenon.

 

[Frame Dragger]

Can you really not see how arrogant and clueless it seems for you to put your own, non-peer reviewed, unverified personal interpretation of Q.M. on the same footing with the standard interpretation that is backed up by 100+ years of solid, peer-reviewed experimental and theoretical literature, and then expect others to do the same?

No, he truly can't, because from everything I've seen he's deeply in the classic "me vs. THEM" scenario. Let's face it, if nearly instant rejection of the submitted paper wasn't hint enough, what is? I'm not joking when I link to definition and explanation of the Dunning-Kruger Effect. I believe it describes a real phenomena, and one that is difficult to ascribe to people who are otherwise NOT deluded. Conway is either young, and lacking insight, genuinely mentally ill, or more likely he lacks the competance to assess his own INcompentence.

@Conway: Sorry, but you're clearly not seeing matters clearly, and while I know this isn't going to phase you at all (nothing will in this fashion), I hope you do educate yourself before you try to educate others. Granted, it's often a mutual process, but you have to find your starting point and work from there, you can't wish for insight into a field and have it arrive via stork.

 

[cesiumfrog]

..you and I have different interpretations. [..] I am not aware of any experiment which distinguishes between my model and your [SpectraCat's] model. Yes, I know your model is consistent with the experimental data: my point is, so is mine.

• Single photon on demand sources. There is an entire field of work which you want to deny has taken place.
• Single electron directed at a panel of detectors. How many electrons can be detected?
• Trees of Stern-Gerlach experiments. You assert that there is no difference between the first two output beams, and hence cannot explain why a series of subsequent apparati would not subdivide the beam further.
• Your conjecture is not an interpretation. Obviously (e.g., single photon source + detector, even if such experiments had not yet been performed) it does not make entirely identical predictions to standard physics theory (and any interpretations thereof).
• Please quit attributing mainstream modern physics solely to SpectraCat. The burden is on you to demonstrate that your claim that your conjecture is compatible with the body of experimental work. By trying to shift this burden back onto the mainstream theory (and by taking a tone that implies your conjecture deserves equal consideration) you will only goad PF's censors.

 

[conway]

I understand there is a growing consensus that I should be barred from the discussion group. I have tried to stay away from personal squabbling but based on the reaction I got for the misuse of a personal pronoun, it's clear that my days are numbered. In the meantime, I'm going to try to stick to the physics and answer as many points as I can in the time remaining to me.

What physical principles is that model based on? Why are such superposition states more believable to you than eigenstates? You need to provide such a basis for your model to be convincing. The fact is that in the absence of a perturbation, the coefficients for your superposition will be time invariant, so a 90% s-, 10% p-state will stay that way forever (or until perturbed).

Spectracat, you have warned me many times against putting myself forward as your equal, so it is with some hesitation that I have to point out that you haven't understood the antenna concept at all. The s-p combination you describe here does not stay that way forever and it does not need a perturbation. If you write the wave function out and follow the charge distribution through time, you will see that it oscillates about the center of mass. That is an antenna; and as an antenna, you can calculate how fast it radiates. It's the calculation I posted yesterday and it is what the atom actually does. Since it is losing energy, the ratio of s to p is continually changing. That's how it ends up in the s state: it radiates away the excess energy that gave it a p component to begin with.

What I am getting at is that you seem to be just picking and choosing a few parts of QM to include in your model (i.e. discrete atomic levels). That will lead to problems when you need to describe phenomena that are not incorporated in your model. For example, what about the selection rule based on conservation of angular momentum? These are experimentally verified. How does angular momentum appear in your model?

For reasons which will not be immediately obvious to you, it turns out that those particular "forbidden transitions" turn out to not have an oscillating dipole moment. It's just one of those things.

What absorption? What equilibrium? In the absence of an energy source, there is a net flow or energy out of the system in the form of photons. So the spontaneous emission of radiation is inherently a non-equilibrium phenomenon.

It's hard for me to know what you're objecting to here. We put the system in a box and the radiation comes to thermal equilibrium with the atoms. I mean, that's the way the calculation is done. I'm not inventing anything here.

You claim your semi-classical model is consistent with the experimental data, but so far you have made a few qualitative arguments and one quantitative estimate that was off by an order of magnitude.

I'm guessing that would tighten up just a little if I used the correct values for the dipole moment, etc.

I have given you some starting points to close this gap ... Rabi oscillations (quantitative, not qualitative), angular momentum conservation rules ... there are plenty of other fine points like spin-orbit coupling and the Lamb shift waiting in the wings.

The Rabi oscillations really are one of the easiest things to explain semiclassically (my motor analogy was a lot closer than you give it credit for), but if you still think that a superposition of 90-s/10-p is stable, then with all due respect there's no basis for me to even try.

 

[Frame Dragger]

Not SPECTRACAT's equal... the equal of the theories and models which he works with. You keep making this personal, but he keeps saying the issue isn't "me/you" or "my model/your model". The issue is, the existing body of work and evidence, and your model/theory/belief.

People are not attacking YOU, they are attacking your ideas. I know,that can seem like the same thing when you're on the recievng end, but that's what it means to have your own theory: constantly defending it, or proving it! In the absence of anything but analogies from you, who's to draw any conclusion, but that you're unable to provide more.

It's fine to have a theory or model or postulate in development, but not to take that par-cooked thing and say "This is MY model, and we'll call The Standard Model 'Your' model." Well, no, because it isn't HIS pet model, it's a major representation of advances in QM and the state of the science.

Finally there is this:

What I am getting at is that you seem to be just picking and choosing a few parts of QM to include in your model (i.e. discrete atomic levels). That will lead to problems when you need to describe phenomena that are not incorporated in your model. For example, what about the selection rule based on conservation of angular momentum? These are experimentally verified. How does angular momentum appear in your model?

For reasons which will not be immediately obvious to you, it turns out that those particular "forbidden transitions" turn out to not have an oscillating dipole moment. It's just one of those things.

That is incredibly rude, or so arrogant that you don't even realize how insulting you've been to someone (Spectra) who's tried for PAGES to meet you even a 10th of the way! You've posted 370 times, you must have seen how quickly the hammer can drop around here; doesn't that tell you: SpectraCat is TALKING to you, not reporting you! In his position, I would have given up by now, as I clearly have.

Again, I'm sorry Conway, because I sincerely doubt you'll listen to, or believe what I'm saying, but everyone here was at LEAST neutral until you worked to make us otherwise.

 

[SpectraCat]

I understand there is a growing consensus that I should be barred from the discussion group. I have tried to stay away from personal squabbling but based on the reaction I got for the misuse of a personal pronoun, it's clear that my days are numbered. In the meantime, I'm going to try to stick to the physics and answer as many points as I can in the time remaining to me.

I for one have never tried to get you banned .. all I have ever done is to try to help you test and improve your models, by providing critical analysis in the field where I have some expertise.

Spectracat, you have warned me many times against putting myself forward as your equal,

I have never done that .. I have stated that I have spent many years working to understand this area of physics as part of my profession. My arguments and criticisms are mostly in the vein of SQM, and thus are inherently well-supported and peer-reviewed. In the few cases where I have been unsure, or have stated matters of opinion, I have explicitly noted those points. My single largest objection to your posts is that you routinely put your half-baked ideas and conjectures on an equal footing with well-sourced, mainstream statements and analyses of myself and others. As I have said, this is unfair to other, less-knowledgeable readers who use these forums as a repository of knowledge, and may not have the experience or context to separate your non-peer reviewed statements from ones that are more solidly based in experimental and theoretical reality.

You also seem to be allergic to posting any math more complicated than basic arithmetic in support of your ideas. Like it or not, math is the language of physics, and every useful/successful theory eventually needs to be supported by a valid mathematical model.

so it is with some hesitation that I have to point out that you haven't understood the antenna concept at all. The s-p combination you describe here does not stay that way forever and it does not need a perturbation. If you write the wave function out and follow the charge distribution through time, you will see that it oscillates about the center of mass.

I assure you that I understand it just fine. I never said that the wavefunction was stationary ... I said that the expansion coefficients for the two basis states don't change in the absence of an external perturbation, which is not at all the same thing. Yes, there is a time dependent oscillation of the charge density in this picture. The oscillation will even also have a non-zero dipole component if you choose a single p-orbital for the expansion. However, as I said, in the absence of an external perturbation, such a superposition will persist forever with no change in the expansion coefficients for the eigenstates. This is basic stuff! Write out the expansion and show me the time-dependence of the coefficients for the superposition state.

That is an antenna; and as an antenna, you can calculate how fast it radiates. It's the calculation I posted yesterday and it is what the atom actually does.

It is a *classical* antenna, and it has no bearing on what an atom "actually does", at least not according to the well-established theory called quantum mechanics. Again, you cannot make your conjectures true simply by stating them .. you need to support them. Quantum physics was largely developed to explain atomic spectra, which defied classical interpretation, and yet you all of sudden want us to accept that atomic emission can be perfectly well-described using a classical antenna model? Forgive us if we don't fall over ourselves to accept your conjecture.

You cannot choose to use just part of QM, and throw away the rest, without some valid reason for doing so. As I pointed out yesterday, the correct classical behavior for the emission of your "atomic superposition antennas" is inconsistent with experimental observation (i.e. quantized emission of radiation from individual atoms) for all cases *except* the pure excited eigenstates, which you claim are an "artifact".

Since it is losing energy, the ratio of s to p is continually changing. That's how it ends up in the s state: it radiates away the excess energy that gave it a p component to begin with.

As I said, it cannot lose energy in the continuous fashion you claim .. it can only lose discrete quanta of energy. This has been verified experimentally. That is part of the reason why the expansion coefficients (10% and 90%) are time stable in the self-consistent, verified, peer-reviewed description given by standard QM.

For reasons which will not be immediately obvious to you, it turns out that those particular "forbidden transitions" turn out to not have an oscillating dipole moment. It's just one of those things.

You need to do better than that ... particularly since I have repeatedly shown that I am more than capable of understanding all the ideas and arguments that you have put forward. (You are being insufferably arrogant with that remark by the way). I am perfectly well aware of how to break down the multipole expansion of a charge distribution, oscillating or not. It is basic spectroscopy. So on this point, I think you are correct and your model will get these selection rules correct, because you are using the atomic eigenstates, which automatically build in the correct description of angular momentum conservation.

It's hard for me to know what you're objecting to here. We put the system in a box and the radiation comes to thermal equilibrium with the atoms. I mean, that's the way the calculation is done. I'm not inventing anything here.

Ok, so we need to define our systems a little better perhaps. I have been focusing exclusively on the case of spontaneous emission, which you claimed your model described correctly, because you said you got the atomic linewidths right. So I am considering the decay of a single excited atom in a vacuum .. no container. At time zero, you have the excited state (in whatever description you choose). At some later time, some of the energy will have been lost to emission ... there is no equilibrium. How does your model describe this?

I'm guessing that would tighten up just a little if I used the correct values for the dipole moment, etc.

Ok, so calculate it out and show us the comparison. Then start providing quantitative predictions for other observed properties of atoms. It was you that claimed, "There is basically nothing that the atoms do in terms of their interaction with the electric field that you can't explain by treating them as little classical antennas." Let's see some more examples.

The Rabi oscillations really are one of the easiest things to explain semiclassically (my motor analogy was a lot closer than you give it credit for), but if you still think that a superposition of 90-s/10-p is stable, then with all due respect there's no basis for me to even try.

There is no "respect" conveyed by that statement at all .. it is completely disrespectful. I have now explained in some detail why superposition states are in fact time-stable in the absence of external perturbations within the framework of SQM. You claim to understand Rabi oscillations, so I would have thought that you would know this, since Rabi oscillations are just a description of how such external perturbations are required to induce time-dependence of the expansion coefficients.

Just to be completely clear, the vacuum fluctuations which give rise to spontaneous emission are considered external perturbations, so SQM correctly predicts emission from superposition states. They are time-stable until the instant that the fluctuation comes into being and perturbs them, at which point they can radiate .. as I mentioned before, this process is effectively instantaneous ... the system goes from excited atom directly to ground state atom + photon in the transition. This is not at all controversial, it is basic first-year QM. So get off your high-horse and support your model.

 

[conway]

I took quite a lot of flak yesterday for suggesting that the pure eigenstates of a hot gas in thermal equilibrium were an artifact of the Copenhagen interpretation. I claimed that it is just as consistent with experiment to assume that all the atoms are in a superposition of eigenstates. I haven't seen anyone post an experiment which shows how you can distinguish these two descriptions. So I'm thinking it might be a nice gesture is someone would acknowledge that I might have been correct on this small point.

(note: cross-posted before I read SpectraCat's reply).

 

[Frame Dragger]

I took quite a lot of flak yesterday for suggesting that the pure eigenstates of a hot gas in thermal equilibrium were an artifact of the Copenhagen interpretation. I claimed that it is just as consistent with experiment to assume that all the atoms are in a superposition of eigenstates. I haven't seen anyone post an experiment which shows how you can distinguish these two descriptions. So I'm thinking it might be a nice gesture is someone would acknowledge that I might have been correct on this small point.

(note: cross-posted before I read SpectraCat's reply).

Conway... have you SEEN me post elsewhere? I'm a massive *******! You want so badly to be everything NOW that you're skipping over things we all have to learn. SpectraCat is trying to teach you, and I'm just trying to get you to really LISTEN to him. No one is trying to ban you, or remove you (or at least, not me, and not Cat). We're not teasing you, and believe me when I say that we could.

Please, take me acting kindly, and SpectraCat not bursting a blood-vessel on more than one occasion, as a sign that we want to help. You're not going to lose face here by admitting ignorance; it's an educational site! That's why I come here, to learn by reading discussions, and sometimes having people with more knowledge (and some FAR smarter) than I correct my misconceptions.

Try this site on its own terms for a bit, and you might be pleasantly surprised.

 

[conway]

As I said, it cannot lose energy in the continuous fashion you claim .. it can only lose discrete quanta of energy. This has been verified experimentally. That is part of the reason why the expansion coefficients (10% and 90%) are time stable in the self-consistent, verified, peer-reviewed description given by standard QM.

Yes, this is what I'm talking about. I don't think there is an experiment which can show this.

 

[Frame Dragger]

Yes, this is what I'm talking about. I don't think there is an experiment which can show this.

That was the problem (arbitrary radiation) which DEMANDED the development of QM in the first place! You could argue that any evidence supporting quantization, supports that.

 

[conway]

I already said that the business of the pure eigenstates is CONSISTENT with experimental observation. That's because people have cobbled together a peculiar way of looking at the world which allows them to disregard the mechanism of how a system gets from A to B. It's called the Copenhagen Interpretation. All I'm pointing out is that this particular feature of the interpretation does not seem to be subject to experimental verification. So I am free to come up with alternative, self-consistent explanation which does not make use of this particular artifact. The fact that my interpretation does not use this artifact cannot therefore beheld as an argument against it.

 

[conway]

For reasons which will not be immediately obvious to you, it turns out that those particular "forbidden transitions" turn out to not have an oscillating dipole moment. It's just one of those things.

I am perfectly well aware of how to break down the multipole expansion of a charge distribution, oscillating or not. It is basic spectroscopy. So on this point, I think you are correct and your model will get these selection rules correct, because you are using the atomic eigenstates, which automatically build in the correct description of angular momentum conservation.

Good insight. I think when I wrote "for reasons which will not be immediately obvious (to you)", what I meant was the reasons were not obvious to me. I just remember evaluating dipole moments for some special cases and having them all come out to zero.\

I still don't understand why you resist accepting the basic antenna premise. You know how to calculate the dipole moments, you know the antenna formulas, and they clearly come out pretty close. Are you saying you think they come out close but not close enough? I haven't sketched out the argument for the B coefficients but I can do that if you want.

The reason I can't do the Rabi calculation is that you still don't accept the premise that if the atomic antenna is absorbing energy, then the p state is growing at the expense of the s state. It's like you accept the calculation of the oscillating dipole moment but deny the fact that Maxwell's equations should apply.

 

[collinsmark]

Hello conway,

I took quite a lot of flak yesterday for suggesting that the pure eigenstates of a hot gas in thermal equilibrium were an artifact of the Copenhagen interpretation. I claimed that it is just as consistent with experiment to assume that all the atoms are in a superposition of eigenstates. I haven't seen anyone post an experiment which shows how you can distinguish these two descriptions. So I'm thinking it might be a nice gesture is someone would acknowledge that I might have been correct on this small point.

I'm not sure anyone is claiming that all the atoms in a hot gas in thermal equilibrium are all in pure energy eigenstates (at least I don't think anybody is claiming this).

Personally, I agree with you that a given atom, that hasn't just released a photon, is far more likely to be in some sort of superposition of energy eigenstates at any given time. Even if the atom is mostly in a eigenstate, there is likely at least a little superposition of other eigenstates, as long as some sort of perturbation has taken place. So yes, in my opinion, I acknowledge you are correct on this.

I think the objection is only in terms of your claim that an electron radiates energy merely by being in a superposition of energy eigenstates.

The way I understand the standard theory is as such. Suppose an atom is prepared into a superposition of two energy eigenstates, say a linear combination of one s and one p, and if then left in a vacuum isolated chamber, it will remain in that superposition state for some time. During this time it will not radiate any energy at all (regardless of the fact that the wave-function's expectation value is oscillating). Then suddenly it will emit a photon which has an energy which is exactly the excitation energy from the s state to the p state (whichever two states were in the superposition). Immediately after the emission, the electron is an energy eigenstate (the s state, in this example). Of course if the atom were then perturbed, by being bumped into another atom, it would go back into some sort of superposition of states (not necessarily like it was before, and not necessarily a superposition of just two energy eigenstates).

The amount of time that the atom remains in the superposition of states (before emitting the photon) is a probabilistic function of the relative amounts of the eigenstates in the superposition. A 90% s and 10% p will statistically last longer in the superposition state than a 50-50% combination. The extra energy that can be thought of as "boosting" the energy up to the p state, such that a photon with the right energy can be emitted, is a function of the quantum fluctuations in the zero-point vacuum energy (that might be a very bad way to put it). Perhaps I should reword that. There is a probability that the electron might be found in the p rather than s state, and that probability determines the statistical lifetime of the superposition state. (It has been said that in QM, there really is no such thing as spontaneous emissions and that all emissions can be thought of as stimulated emissions -- the spontaneous emission case is really just a special case of stimulated emission, where the emission was stimulated by the zero-point vacuum energy.)

The point of all of that, is when it comes to electromagnetic radiation of an electron in a superposition of states, it's either all or nothing. Either the atom remains in the superposition -- radiating nothing, or it emits a photon which has an energy equal to the difference in energy between the two energy eigenstates in the superposition. The ratio of the relative eigenstates in the superposition has no bearing on the photon's energy (well, assuming that the two energy eigenstates are both at least present to some degree) -- it only has an impact on the amount of time it takes for the superposition state to decay. Or in the case of stimulated emission, it affects the probability that stimulated emission will occur.

This is experimentally verifiable. It can be performed with a trip to the Radio-Shack(TM), and a purchase of a small neon bulb, a current limiting resistor, and a diffraction grating or prism. I'm guessing the cost of the experiment materials might be under around $15. Attach one of the resistor's leads to one lead of the neon bulb. Plug the spare leads into a nearby wall socket. Use the diffraction grating or prism to view the spectrum. You'll notice that the only light is in very, very narrow bands in the spectrum. The difference between these bands corresponds to certain excitation energies between different energy eigenstates of neon.

If an electron, in a state of superposition between two energy eigenstates were to continuously radiate (such as gradually becoming less of p and more of s), the resulting spectrum would be more continuous, and you wouldn't see the discrete bands. But continuous (broader) bands are not observed in the $15, Radio-Shack(TM) experiment. The observed data show the radiated bands are very, very narrow.

(All this of course hinges on accepting the idea that E = h \nu, but that's been quite well established going back to 1905.)

[Edit: Sometimes it is advantageous to approximate atoms as only being in pure energy eigenstates, if one is not concerned about position and momentum, and if nearly all of the measured interactions only deal with energy. In QM, what you measure is what you get -- if you measure energy, the wave-function appears to collapse to to an energy eigenstate. If you measure position, the wave-function appears to collapse to a position eigenstate (which resembles a Dirac delta function, and is necessarily a superposition of energy eigenstates). But if nearly all the interactions of the experiment involve energy, and the measurements involve energy, then approximating everything as only being in pure energy eigenstates is often useful. It certainly simplifies things a lot. On the other hand, this approximation can mislead students into believing that atoms only occur in pure energy eigenstates. It is common for 1st year chemistry students to mistakenly believe that electrons in atoms only occur in these well defined electron orbitals or clouds (represented by the energy eigenstates), and that's it. We know that the shape is quite different (and time varying) when things are in superposition. But the misconception still persists. In all fairness though, even if it is a misconception, it still holds up pretty well as an approximation if the only thing that is of any concern is energy.]

 

[conway]

Hi Mark

Thanks for taking the time and effort to write such a detailed explanation of the emission process. You deserve some credit for being the first one to step up to the challenge of identifying an experiment which refutes my point of view. I’m sorry to have to tell you that I can’t agree with your refutation. I’ll try to explain why.

First of all, I am glad that you agree that atoms can be in a superposition of energy states, and that those superpositions will often (as in the s-p case) lead to an oscillating charge distribution (not to quibble but you call it an “expectation value”). I think you are onside with Spectracat so far.

What I am only beginning to grasp is that both you and Spectracat, while allowing the charge distribution to oscillate, do not allow the electron to radiate as an antenna. I find this perspective utterly baffling, and consider it to be the worst of both worlds vis-a-vis the Schroedinger versus the Born interpretations. (I hope this is neutral enough: I’m going to refrain henceforth from calling them “my wave interpretation versus your Copenhagen interpretation.) You retain the “quantum leap” of the old Bohr atom even though the Schroedinger atom makes it unnecessary by allowing for an orderly passage between eigenstates via time-evolution.

You say: “I think the objection is only in terms of your claim that an electron radiates energy merely by being in a superposition of energy eigenstates.” Correct; and this claim is in fact the central pillar of my worldview. I sink or swim with it.

You further state: “The point of all of that, is when it comes to electromagnetic radiation of an electron in a superposition of states, it's either all or nothing. Either the atom remains in the superposition -- radiating nothing, or it emits a photon which has an energy equal to the difference in energy between the two energy eigenstates in the superposition.” Again, hits at the crux of my worldview: in my picture, the antenna is radiating continuously, so long as the superposition persists. The amount of energy radiated is arbitrary: in the absense of the external field, it will radiate all the available energy (one-half a quanta for a 50-50 superposition) until it stabilises in the ground state; in the presence of an ambient field, it will either emit or absorb energy as the as the phase of the driving field leads or lags the phase of the oscillating charge.

I have shown that with my model I can easily estimate the emission rates (the Einstein A coefficient) by a simple ballpark calculation. I can do the B coefficients as well if anyone is interested. So my model does not claim to give different results than the standard model.

Now let me address your counterexample of the neon lamp’s emmision spectrum. You believe that the continuously oscillating expectation value would give rise to a distributed spectrum. I’m understanding you see it as something like the Bohr atom where the orbit spirals inwards at higher and higher speeds; correct me if I’m wrong. In any case, this is not what the Schroedinger equation gives me. The frequency of charge oscillation is constant throughout the transition, and it is the difference of the ground state and excited state frequencies. Tell me if you need me to elaborate on this, because it should be quite straightforward from the expression for the wavefunction. The result is that my tiny antennas give exactly the same spectrum as your “quantum leaps”.

Finally: I really, really don’t like to invoke authority in these discussions. I think what’s wrong with physics these days is that everything is about what papers you can quote. People are throwing citations back and forth and there’s not that much actual physics being argued. I like to think my arguments should stand or fall on their merits and not on whom I can reference. But it is also a fact that starting in the 60’s a research group led by Jaynes did a lot of work to see just how far you could go using the combination of classical light and the quantum atom. I’m sure people here have vaguely heard of this, at least anecdotally. I wonder what people think they came up with if it wasn’t basically the kind of things I am talking about? I’ve never read any of their stuff myself but if they didn’t deal with my little atomic antennas, then I can’t imagine what they spent their time on.

 

[collinsmark]

Hello conway,

I've been thinking about this since my last post, and perhaps I have some insight that might help you if you decide to continue the theory you've been working on, partially involving atom's acting like antennae.

You've mentioned that antennae described in your model have an extremely high Q.

Let's consider a macroscopic, ideal antenna that has nearly infinitely high Q at certain frequencies. If you were to attach a signal generator to this antenna, it would only radiate power at these certain frequencies. Since it's an ideal antenna, at these frequencies it would radiate energy with 100% efficiency. But at any other frequencies, the power would be purely reactive, and it would transmit nothing. When the signal generator is not at one of these specific frequencies, the antenna does not radiate, but it does not draw any real power from the signal generator either (it's acting like an ideal capacitor or an ideal inductor; or perhaps like an open circuit). So the antenna is still 100% efficient. No power is ever wasted by the antenna.

The antenna can also be used for reception too. If the electromagnetic field around the antenna is exactly one of these frequencies, a voltage will be produced at the antenna terminals, which can be used to gather real power from the electromagnetic field. But if the field is at any other frequency, the thing is useless as a receiver.

Now let's shrink this infinite Q, ideal antenna down to the size of an atom, and bring up the superposition of the s and p eigenstates. Let's also accept the relationship of E = h \nu. Suppose the tuned frequencies of the antenna conform to \nu = E/h and the energy E corresponds to the excitation energies of the atom between the ground state and excited states.

If the electron was in an excited energy eigenstate, it would have enough energy to produce one of the tuned frequencies of the antenna and emit a quantum of energy. But as soon as it did so, the available energy would drop according to E = h \nu, and the available energy would correspond to a lower energy eignenstate, where another quantum of energy might be emitted (at a different tuned frequency), until eventually the energy reaches the ground state.

Now let's imagine that the electron is in a superposition of states. Suppose it is in a superposition between its ground state and the first excited state. Would it be able to radiate this extra exited energy to other atoms around it? No! Because the available energy isn't enough to correspond to one of the antenna's tuned frequencies (via \nu = E/h). The energy just stays in the atom. The atom does not radiate! Just like in the case when it was bigger, the antenna doesn't transmit any energy, but it doesn't draw any energy from the atom either. Could the atom receive just enough energy (via the antenna) to get to one of the tuned frequencies? Not exactly, but it could go past the amount by receiving the right quanta of energy, in which case it would simply be in a superposition of different energy eigenstates (although now it could release a particular quantum of energy).

The point of all of this is that even using your semi-classical model where atoms act like high Q antenna, the atom will still only radiate energy having specific quanta. This is almost just like photons. And it sort of agrees with some experimental evidence.

Of course, once again, it all hinges on E = h \nu.

So I believe that if you continue your theory, you'll ether have to abandon the idea that electrons/atoms continuously radiate energy merely by being in a superposition of states, or abandon E = h \nu as well as Einstein's photoelectric effect (and perhaps anything in quantum mechanics that is based on such results).

[Edit: When I wrote the above, I was assuming that the antenna's tuned frequencies are somehow tied to the state that the electron happens to be in (superposition or not). Re-reading the above I seem to have left this out. If they were totally independent, the atom could release energy quanta corresponding to higher excited states (lower frequency spectra -- still quantized though) even though the electron was near the ground state. If you were to power a filament in a bulb, the radiation spectra would first behave as if the electrons were in a highly excited state, only to produce the lower state quanta wavelengths only when the gas became very hot -- totally backwards from experimental data! But that's not what I meant when I wrote the post. What I neglected to say was that the quanta that the electron can radiate or absorb would need to be tied to the state of the electron. Given that, the above post still holds, and the antenna-model atom would not continuously radiate merely by being in a state of superposition. Anyway, thinking about all this is just giving me a bad headache. Sorry conway, but I think you're on your own on this one.]

 

[conway]

SpectraCat, I hope I am not misrepresenting your last post when I say that you seemed to accept my characterisation of the superposition of s and p states as an oscillating charge distribution, but maintained that it would not radiate energy energy in a continuous way, antenna-style, while in that state:

Yes, there is a time dependent oscillation of the charge density in this picture. The oscillation will even also have a non-zero dipole component if you choose a single p-orbital for the expansion. However, as I said, in the absence of an external perturbation, such a superposition will persist forever with no change in the expansion coefficients for the eigenstates. This is basic stuff! Write out the expansion and show me the time-dependence of the coefficients for the superposition state.

And later you continue:

"As I said, it cannot lose energy in the continuous fashion you claim .. it can only lose discrete quanta of energy. This has been verified experimentally. That is part of the reason why the expansion coefficients (10% and 90%) are time stable in the self-consistent, verified, peer-reviewed description given by standard QM. "

And you conclude:

“Just to be completely clear, the vacuum fluctuations which give rise to spontaneous emission are considered external perturbations, so SQM correctly predicts emission from superposition states. They are time-stable until the instant that the fluctuation comes into being and perturbs them, at which point they can radiate .. as I mentioned before, this process is effectively instantaneous ... the system goes from excited atom directly to ground state atom + photon in the transition. This is not at all controversial, it is basic first-year QM. So get off your high-horse and support your model.”.

Surely you are not claiming that this is the Copenhagen interpretation? Unless I’m very wrong, I thought according to Copenhagen, the atoms were distributed between the discrete energy levels, all of them in pure eigenstates, no superpositions, and the photons are emitted instantaneously as the atom jumps between energy levels? Or is what you’ve called “SQM” different from what I think Copenhagen is?

It just doesn’t add up to me. I can see Copenhagen somehow trying to make do with time-stable eigenstates that instantaneoulsy jump from one level to another: I don’t like it but I suppose it’s consistent: the eigenstates are not antennas, so to get from one to the other they must make some magical transition. But I can’t see how SQM would allow superpositions of those eigenstates and then compel them to remain time-stable rather than simply allowing them to radiate according to Maxwell’s equations. Are you sure you’ve got it right?

 

[SpectraCat]

SpectraCat, I hope I am not misrepresenting your last post when I say that you seemed to accept my characterisation of the superposition of s and p states as an oscillating charge distribution, but maintained that it would not radiate energy energy in a continuous way, antenna-style, while in that state:
And later you continue:
And you conclude:
Surely you are not claiming that this is the Copenhagen interpretation? Unless I’m very wrong, I thought according to Copenhagen, the atoms were distributed between the discrete energy levels, all of them in pure eigenstates, no superpositions, and the photons are emitted instantaneously as the atom jumps between energy levels? Or is what you’ve called “SQM” different from what I think Copenhagen is?

It just doesn’t add up to me. I can see Copenhagen somehow trying to make do with time-stable eigenstates that instantaneoulsy jump from one level to another: I don’t like it but I suppose it’s consistent: the eigenstates are not antennas, so to get from one to the other they must make some magical transition. But I can’t see how SQM would allow superpositions of those eigenstates and then compel them to remain time-stable rather than simply allowing them to radiate according to Maxwell’s equations. Are you sure you’ve got it right?

Yes, I am sure. You are confused about several things. There is no restriction in SQM or CI for "pure eigenstates". When you start from a system of pure eigenstates as is typical, then you can create superposition states IF AND ONLY IF a time dependent perturbation is present that can couple the levels .. that is a big part of what Rabi oscillations *are*. They describe the smooth oscillation of the superposition between the ground and excited states of a two-level system, at a frequency which depends only on the magnitude of the perturbing field. If the oscillations are going, and then the perturbing field is switched off, the system becomes "trapped" in whatever particular superposition it was in at that instant (say, the 90-10 example we have been discussing). This system will persist as a stable superposition state until it is perturbed somehow, say by a vacuum fluctuation to initiate spontaneous emission as I have described.

By playing clever tricks with photon phase and polarization, physicists can actually use this to create superpositions involving "dark states", which have no route to decay by photoemission, and thus can persist for arbitrarily long times. I have not studied these papers in detail, but I think the gist of the technique is they set the system into a Rabi oscillation using the optical excitation, and then quickly switch the light off when the phase of the Rabi oscillation corresponds with zero coefficient for the bright state. However the states are prepared, the important point for the current discussion is that, since the coefficients can't change after the field has been switched off, the system is stuck in that superposition state, and can't decay, because the dark states do not have any allowed routes back to the ground state. I can't see any hope of describing such a process using a classical antenna model for atomic absorption.

You are getting hung up on the oscillating charge density, because you are thinking about the system classically. There is nothing classical about it. Maxwell's equations in the classical form you are referring to do not apply ... you need to use the versions for quantized fields in order to properly describe the emission. I am not an expert in QFT, and I don't really know how to do that. However, I do understand the proper semi-classical description (classical fields, quantized electronic states), and I understand the phenomenology of spontaneous emission. That is what we need to address your example, as I have been saying.

An important point that you may be missing is that I am most emphatically *not* saying that superposition states will not radiate ... they will definitely radiate by spontaneous emission as follows. When the system is in a superposition state, the squared coefficients describe the probability that a measurement will cause the system to be "resolved" into the various component states due to decoherence. As I understand it, that is what happens when a vacuum fluctuation initiates spontaneous emission ... in the case of a superposition state, if the interaction "resolves" the system into the ground state, nothing happens .. it is already stable. However if the fluctuation perturbs the system into the excited state, then it can decay to the ground state via the emission of a single photon. Thus the probability of spontaneous emission from such a state is described by the normal Einstein A coefficient, multiplied by the probability of finding the system in the excited state.

Finally, in your reply to Collinsmark, you wrote:

You say: “I think the objection is only in terms of your claim that an electron radiates energy merely by being in a superposition of energy eigenstates.” Correct; and this claim is in fact the central pillar of my worldview. I sink or swim with it.

You are going to sink, because that picture is incorrect for quantum systems, as I have been trying to explain to you. Please, for both our sakes, write down the time-dependent wavefunction describing the two-state superposition of s and p states that *you* introduced as part of your system. Examine it carefully, and try to find the time dependence of the expansion coefficients .. you cannot, because it is not there. The time dependence has to be induced by an external perturbation ... research time-dependent perturbation theory a bit and hopefully you will be able to understand this a little better.

 

[conway]

Yes, I am sure. You are confused about several things. There is no restriction in SQM or CI for "pure eigenstates". When you start from a system of pure eigenstates as is typical, then you can create superposition states IF AND ONLY IF a time dependent perturbation is present that can couple the levels...

SpectraCat, I think I was trying to get onside with what you called "basic first-year QM". In this quote you refer to a system of pure eigenstates as "typical". So was I at least more or less correct in describing SQM's version of say, an hot gas in thermal equilbrium with radiation inside a box? So the gas molecules are distributed between the ground states and the excited states according to A*exp(-E/kt), with basically no atoms in a superposition?

You are getting hung up on the oscillating charge density, because you are thinking about the system classically. There is nothing classical about it. Maxwell's equations in the classical form you are referring to do not apply ... you need to use the versions for quantized fields in order to properly describe the emission. I am not an expert in QFT, and I don't really know how to do that.

But didn't I get pretty close to the correct emission rate with my ballpark calculation of radiation resistance for the short antenna?

However, I do understand the proper semi-classical description (classical fields, quantized electronic states)...

Are you talking here about the research led by Jaynes starting in the 1960's which I mentioned a couple of posts back? I have never read their papers but I can't imagine what they could have been doing unless it was just the type of things that I am talking about, calcuating radiation resistance for small antennas etc. Would that not be the proper semi-classical description?

Please, for both our sakes, write down the time-dependent wavefunction describing the two-state superposition of s and p states that *you* introduced as part of your system. Examine it carefully, and try to find the time dependence of the expansion coefficients .. you cannot, because it is not there. The time dependence has to be induced by an external perturbation ... research time-dependent perturbation theory a bit and hopefully you will be able to understand this a little better.

It's true that the coefficients are not time dependent. But that's just because you derive those coefficients using an incomplete formula, i.e. Schroedinger's equation, that doesn't include a term for electromagnetic radiation, so your expression for the time evolution is only an approximation. The time variation of the coefficients comes in naturally when you include the effect of Maxwell's equations on the system.

 

[SpectraCat]

SpectraCat, I think I was trying to get onside with what you called "basic first-year QM". In this quote you refer to a system of pure eigenstates as "typical". So was I at least more or less correct in describing SQM's version of say, an hot gas in thermal equilbrium with radiation inside a box? So the gas molecules are distributed between the ground states and the excited states according to A*exp(-E/kt), with basically no atoms in a superposition?

Yes and no ... the *average* distribution is given by the Boltzman factors in terms of pure quantum states, but at any instant in time, there can certainly be atoms in superposition states, since there are time-dependent perturbations (i.e. the radiation fields), available to mix the states. Remember that the superposition states will decay due to spontaneous emission, they just won't do it as quickly as the pure excited states. (Note: I will have to classify my position on that last statement as "pretty darn sure but not certain" ... I think one really needs to use QFT to get the correct answer, and I am not facile enough with QFT to work out the answer without a significant amount of work that I don't have time for right now).

But didn't I get pretty close to the correct emission rate with my ballpark calculation of radiation resistance for the short antenna?

So what? I pointed out several other flaws with the physics of that model (which have been corroborated by others), so I am inclined to believe that it was just coincidental. I'd want to see a more detailed analysis, and a couple of other successful predictions before I am willing to accept that it was more than a coincidence.

Are you talking here about the research led by Jaynes starting in the 1960's which I mentioned a couple of posts back? I have never read their papers but I can't imagine what they could have been doing unless it was just the type of things that I am talking about, calcuating radiation resistance for small antennas etc. Would that not be the proper semi-classical description?

No, I am talking about the same semi-classical picture that is typically used in spectroscopy to derive formulae like the Rabi formula and Fermi's Golden rule for transition rates. You assume that the EM field is classical, with a continuous amplitude that represents the magnitude of the perturbation coupling the quantum states. It is much older than the 60's .. it dates back to Einstein and Dirac. I am unfamiliar with Jaynes' papers, but I will look then up when I have time.

It's true that the coefficients are not time dependent. But that's just because you derive those coefficients using an incomplete formula, i.e. Schroedinger's equation, that doesn't include a term for electromagnetic radiation, so your expression for the time evolution is only an approximation. The time variation of the coefficients comes in naturally when you include the effect of Maxwell's equations on the system.

Schrodinger's equation may be incomplete, but I don't agree that you can apply the classical versions of the Maxwell equations to this system .. at least not to get physically sensible results. However, if you are saying that theories incorporating quantum descriptions of Maxwell's equations such as QFT or QED can supply a better description of this problem, then by all means I agree with that statement. I have not worked through those derivations for myself for a rather long time, but as I recall it, what you get from those treatments is Einstein's A-coefficient for spontaneous emission. As I have said, that is why I feel justified using it in the context of our current discussion, and I believe I have interpreted it's significance correctly.

 

[Cthugha]

Are you talking here about the research led by Jaynes starting in the 1960's which I mentioned a couple of posts back? I have never read their papers but I can't imagine what they could have been doing unless it was just the type of things that I am talking about, calcuating radiation resistance for small antennas etc. Would that not be the proper semi-classical description?

In fact Jaynes did quite the opposite. The famous Jaynes-Cummings model (THE model of quantum optics) describes the interaction of a quantized two-level atom with a quantized cavity field mode and they tried to find out which differences occur compared to the semiclassical model. For example the semiclassical model can explain Rabi cycles of probabilities, but not stuff like revivals of population inversions after a collapse and vacuum Rabi splitting for single emitters in a cavity.

 

[conway]

Cthuga, I appreciate your input, but I don't understand it, especially your use of the phrase "just the opposite". You say they compare the quantized two-level atom with a quantized cavity field mode (call this A) to the semiclassical model (B). Are you saying they compared A to B and found B could explain some but not all? That's what I understand...that A is SQM and B is "semiclassical".

If I've understood that correctly, that I have to ask again: just what was the "semi-classical model" they used if not my little antennas with their radiation resistance etc? I'd really like to know.