Why does decoherence not fully solve the measurement problem?

[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.