Electron Transitions and the Uncertainty Principle

[selfAdjoint]

hilbert space certainly exists (there's no mathematical problem to have a tensor product of 10^25 single-particle hilbert spaces, as far as I know)

That's "exist" in the mathematical sense that there is a conceptual model. Existence in any other sense is precisely the Platonic issue, no?

 

[vanesch]

That's "exist" in the mathematical sense that there is a conceptual model.

But this is what I thought what masudr was talking about when he said:

In fact, I believe that some proofs do not even exist in the "platonic mathematical world", as vanesch put it, and we might even be able to prove that some conjectures are unprovable.

I was wondering what he had in mind that could be potentially unprovable.

 

[masudr]

Sorry, I was talking more about the limitations of using a universal turing machine in performing the computations. Whilst a UTM can perform any task any computer can, it may require an infinite amount of tape/processing time which may well not be a feasible requirement. Also, there are some algorithms that a Turing Machine can never compute (the canonical example being whether or not a particular program on a turing machine will halt or not).

 

[reilly]

Re atomic transitions: you can nicely describe the complete transition from beginning orbital to final orbital with emission (or absorbtion) of a photon by means of standard time-dependent QM. This was discussed, in a ground-breaking paper, by Wigner and Weisskopf in the 1920s or 1930's, and is a topic widely discussed in the research literature and textbooks. I'll recommend the books on QED by Cohen-Tannoudji, Dupont-Roc and Grynberg, in which the issue of atomic transitions involving photons are described in extraordinary detail. Everything you want to know is there -- some of it is not easy. You pose a problem that's been well understood for close to a century, and is, in fact, central to much of field theory and particle physics.

Other names that are relevant are scattering theory, resonance production and decay, nuclear transitions.

Within the spirit of QM theory, you can always find the electron, before, during or after the transition -- well sort of --. The key, in this regard, is the typical time integral that gives the ubiquitous 'finite delta function",
sin(dE*t)/dE, where dE is the energy difference between the final and initial states. As long as the "time length of the experiment, t, is finite, then the electron can be in either the initial or final state, as in a superposition. We are getting farther into S matrices and scattering theory than I anticipated.

There's, as I said earlier, a huge literature on this subject -- do a Google on Wigner-Weisskopf, Breit-Wigner, resonances, resonant scattering, line breadth, radiative reactions, scattering theory, atomic and nuclear radiation, quantum optics, ...

How does the transition happen? With absorbtion, the energy of the electron changes, and thus changes must occur in the wave function -- usually described by means of time-dependent perturbation theory -- due to the governance by the systems' Schrodinger equation. Given the right tools, QM does a very nice job of describing the evolution of an atomic transition in a blow-by-blow fashion. That is, the Schrodinger Eq gives a complete account of the evolution of the wave function, and hence of the probabilities governing possible experiments.

Regards,
Reilly Atkinson

 

[rewebster]

Electron transition may be the result when a photon is absorbed or emitted, but how is it transitioned is another question.

Just as: what actually happens to the electron when a photon is absorbed as to make it different?

What happens to the photon as it is being absorbed into the electron?

Why can a photon be absorbed in the first place?

How can the photon be emitted from the electron (what mechanism re-assembles the photon?)

Is the photon emitted the same photon that was absorbed? (If not, how is it different and where did it come from?)

Can the photon be absorbed by the nucleus? --can the emitted photon from one electron be absorbed by an electron in the same atom?


These are just a few of the questions that I think about-------

 

[ZapperZ]

Electron transition may be the result when a photon is absorbed or emitted, but how is it transitioned is another question.

Just as: what actually happens to the electron when a photon is absorbed as to make it different?

What happens to the photon as it is being absorbed into the electron?

Why can a photon be absorbed in the first place?

How can the photon be emitted from the electron (what mechanism re-assembles the photon?)

Is the photon emitted the same photon that was absorbed? (If not, how is it different and where did it come from?)

Can the photon be absorbed by the nucleus? --can the emitted photon from one electron be absorbed by an electron in the same atom?


These are just a few of the questions that I think about-------

While you are thinking about it, you may want to correct a few errors.

An electron does not absorb a photon. It can't do that. The "absorption" is done by THE WHOLE ATOM. You'll notice that when you solve for the atomic energy level, the whole atom is involved, not just a single electron. A single, free electron does not exhibit the atomic energy level - that's why we call it "atomic" energy level.

So the "devil" is in the details. One needs to really look at the basic physics and get it clear first before asking about the next step in understanding the phenomenon. Or else, you'll be working from a wrong premise.

Zz.

 

[rewebster]

Isn't the whole atom really the electrons and the nucleus (the parts make the whole)?--I did include both in the questions

If you threw a small ball into a group of people, and it was caught, --it had be caught by an individual --not the entire group (yes, I know this deals with a level of quantum)?---does the ball (photon) degrade?

So does the photon get absorbed by the nucleus,and/or the electons; and if, by the entire atom, --still, how is it 'absorbed'?---what happens to it? where ever it goes?

Is the result always an electron transition? why is an electron transition the visible evidence of an absorbed photon?

Absorbtion, at what is termed, 'the atomic level', seems vague to me. So, if the absorbtion happens at all, then, other actions do take place.

 

[rewebster]

Another analogy:

Ask a person where they went, and they may say. " I went to town."

Ask them, what exactly did you do all day?----and they'll have a different answer.

 

[ZapperZ]

Isn't the whole atom really the electrons and the nucleus (the parts make the whole)?--I did include both in the questions

Look at the post I was referring to. You specifically mentioned electrons absorbing photons. These violates several conservation laws.

It is an atom that absorbs a photon, or in the case of solids (as in the photoelectric effect), it is the whole solid band structure that absorbs the photon. All you need to do is look at a single, free electron, and tell me what energy level it has to be able to make the transition to absorb such energy AND the ability to account for absorbed angular momentum.

If you threw a small ball into a group of people, and it was caught, --it had be caught by an individual --not the entire group (yes, I know this deals with a level of quantum)?---does the ball (photon) degrade?

And how does THIS correspond to a quantum mechanical scenario? Do you think a photon is a "ball"? Do you think electrons have hands? To what extent to you think your analogy is valid to be applied to this case? Are these people describable by a QM wavefunction? Just because you can come up with an analogy doesn't mean it has any validity to the scenario here. The whole idea of QM is that it DEFIES classical description that you hold so dearly. It is why it isn't easy!

So does the photon get absorbed by the nucleus,and/or the electons; and if, by the entire atom, --still, how is it 'absorbed'?---what happens to it? where ever it goes?

By the atom!

Is the result always an electron transition? why is an electron transition the visible evidence of an absorbed photon?

Look, the energy absorption causes the atom to be in an excited state. This is manifested by an electron making a transition to a higher energy state. These energy states does not exist without the consideration of the whole atom.

The nucleus has its own energy level, but these are at a significantly higher energy than what we are used to. Nuclear processes are not what you asked for her and not what I was intending to correct. I simply wish to correct the very frequent misconception that in many optical processes that it is the electron doing the "absorption". This is false. If you cannot get pass this, then there's no point in going any further.

I suggest you look up a simple case of a hydrogenic atom and look at how QM treats that case and how the solution to all the atomic orbitals and energy levels were obtained. Only in such a detail can you satisfy yourself that the Coulombic potential is a necessary part of the ingredient and how the selection rule is clearly satisfied. There's nothing vague at all here.

... and enough with the analogy already!

Zz.

 

[jtbell]

Isn't the whole atom really the electrons and the nucleus (the parts make the whole)?

The whole is "more" than (or at least different from) the sum of its parts.

 

[rewebster]

Do I think that it is the electron that absorbs or emits the photon?--no

What I was pointing toward all along is that the photon has to hit 'something' and that the photon is changed to another form in the atom (the atom and its 'field'---and the word 'field' means a lot of things). The word 'energy' loss/gain is used quite often and is singularly ambiguous as to connotate or correlate what is the mechanism behind what happens to it. The result is observable. The mechanism of its conversion is what is to be described.


Analogies are always ambiguous.

 

[chroot]

The word 'field' actually means exactly one thing, when used by a physicist.

I'm not even going to speculate on what 'singularly ambiguous' means, but it's obvious that you're throwing around scientific words and concepts with almost zero actual understanding of what they mean.

Beware that overly-speculative posts are not permitted on physicsforums, and you may lose your posting priveleges here if you intend on posting such material.

- Warren

 

[rewebster]

I was thinking that in the 'field' definition that it could include electric, gravitational, magnetic, radiation, and/or ion.


And that energy loss and/or gain could be any change in any/many of the above at anyone time; and, that most of the above are theoretical.


I'm not sure how I was overly-speculative. Do you mean by asking the question about the mechanisms behind them?

 

[reilly]

If you look carefully, not only does the electron absorb a photon, but every proton and neutron in the nucleus can absorb the photon -- the QED Hamiltonian has a three point charge-photon interaction for every particle involved. Yes, the dynamics of the situation enter and matter to insure the appropriate conservation laws. And, there is quite a substantial literature on the subject of electron-photon scattering -- it was well discussed by Mott and Massey in the late 1930s in the classic Theory of Atomic Collisions. See also Goldberger and Watson's Collision Theory.

As far as the questions about the how of absorbtion and timing, there are answers. First, QED is formulated from the very start to enable photon absorbtion and emission by charged particles -- the classic three-point interaction of QED is an assumption; absorbtion and emission of photons are built in from the beginning. All the questions about timing can be answered with time-dependent QM -- it's all about the evolution of the possible final states. Good homework problem.

Regards,
Reilly Atkinson

 

[rewebster]

reilly--


is there any validation anywhere for the three axial models?

or toward the 'exactly' same (frequency, at least) emission of a photon after absorption?

 

[rewebster]

Photons, in the classic sense, can be transmitted through, refracted, absorbed, or reflected in/through/back from a material. One of the more interesting is that is a photon can be 'reflected', as from a mirror. I've read how a mirror is made with the 'silver' liquid, polarizing as it dries, to make the mirror surface. I asked a couple physicists (not on the forum) why a mirror reflects light on an atomic level--

is the photon actually reflected?--bounced back?

is the photon the same one that bounces back?

is the photon absorbed and then transmitted off at a 'mirror' angle?



I never got an answer that resolved it for me.

This goes back in the thread to whether and where in the atom the photon is 'handled' in the atom, and its puzzled me for over twenty years. I have my own GUT (which I guess I won't not put any part on the forum, due to it will be considered too overly-speculative by many, it's best not to cause problems). I can get a grasp on absorption, transmission, refraction--but perfect 'mirror reflection' of the photon wave/particle (whatever the personal taste) on the atomic/ sub-atomic level still eludes me.

 

[CrusaderSean]

photon is a boson (identical particle) so you can't distinguish which photon it is. I haven't dealt with photons in quantum mechanics yet, but my guess is it's just reflected.

 

[rewebster]

The thing that bothers me is the perfect reflection of the photon---even considering the Kasimir effect (below)---a change in velocity of 2c without effecting the wave/particle (photon) in any known form (wavelength, 'energy', etc.) or the reflective material is the unusual aspect. And this, again, goes back to the structures and/or 'fields' and/or a combination of these of the atom and of the photon that make it possible for the 'reflection' to occur.


"http://focus.aps.org/story/v7/st5"

"http://prola.aps.org/abstract/PRL/v86/i6/p987_1"

 

[Terry Giblin]

Who said?

"An electron does not exist, until it is observed".

Everyone should listen to what he said and then try to understand what it means, then perhaps questions of this nature would not appear.

The electron disappeared or calasped the instance we interferred or observed it, as soon as it reached the first quantum barrier it became a quantum electron and tunneled its way through.

Regards

Terry Giblin

small and easy question !

in any quantum system, harmonic oscillator, atom, or any other we know the electron can be found on a specific orbits or shells, and can't be found between them right?

how does it go from a shell to another when it's excited for example? does it disappear from the one and appear in the next one? or it moves normally until it reaches the next shell like me when i go from my room to the house door (that's impossible as quantum says)? what then? how does it change it's position? lol ! that's magic !

Anyone can explain?

 

[ZapperZ]

"An electron does not exist, until it is observed".

Everyone should listen to what he said and then try to understand what it means, then perhaps questions of this nature would not appear.

The electron disappeared or calasped the instance we interferred or observed it, as soon as it reached the first quantum barrier it became a quantum electron and tunneled its way through.

Regards

Terry Giblin

No, this is meaningless.

You don't observe an electron. You observe the PROPERTIES that are defined to be an electron. What do you think is in "superpostion"? The electron? NO! Write down the wavefunction of ANY electron in ANY configuration. You will see that what is in superposition is the OBSERVABLES associated with an electron. This is how an "electron" is DEFINED, by a set of properties. And if you think about it carefully enough, you'll realize that EVERYTHING that we consider to exist is based on the existence of a set of properties that defines that object.

So to say that the electron "disappears" (we're not talking about some virtual particle here) or reappears as part of its superpostion is wrong.

Zz.

 

[rewebster]

I'll get off the photon 'reflection' for a "quick"--(really quick) question:

This may have been answered somewhere, but----when an electron moves from one shell to the next [you pick a shell--direction doesn't matter (too much) for this question-(in being extremely exact, I think it would though)]---if it moved (jumped) at the speed of light (I wouldn't guess that it would, but in this question, just for a hypothetical standpoint)----how long would it take?

 

[Terry Giblin]

Stats Probability density function (1-p)

ZapperZ, thank you for your last comments and pointing out my wrong choice of words, but you are absolutely correct, an electron does not exist only the properties, which we associate with electrons.

"An electron (or should I say its properties) only exist, when it (they) are observed."

But what about the properties that we cannot measure or simply ignore, as in the case of the flatlanders?

Or perhaps we are looking at everything from the wrong perspective.

In statistics, you normally calculate the probability of an event occurring, however sometimes it is easier to calculate to probability of the event Not happening and subtracting it from 1.

How would you calculate the probability of an electron tunnelling through an infinite number of quantum wells, its easier calculate the probability that it doesn't happen and subtract from 1.

But the result becomes meaningless, if we only measure success when the electron properties appear, what about the other 99.99% chance that they did not appear 1 - 1 = 1, only if -1 is imaginary.

Its the only way you can get a square peg in a round hole and we have already proven it works, its amazing what you can convince yourself of applying reverse logic.

Regards

Terry Giblin

 

[ZapperZ]

ZapperZ, thank you for your last comments and pointing out my wrong choice of words, but you are absolutely correct, an electron does not exist only the properties, which we associate with electrons.

"An electron (or should I say its properties) only exist, when it (they) are observed."

But what about the properties that we cannot measure or simply ignore, as in the case of the flatlanders?

What exactly are the properties of electrons that cannot be measured?

Zz.

 

[-Job-]

Does a photon curve space-time, even if just a little? If they do, then from now on to me they're just tiny massless space-time bumps, it's easier for me this way.

 

[rewebster]

On my question in 51 and in relation to the electron 'jump':

What I was moving toward was two possibilities.

The first, taking one given radius of the hydrogen atom and hypothetically taking it as the distance between shells (I haven't found anything on the measured distances between shells) in a Copernican based model, the time may be around 5 x 10 to the minus 21 sec. for the electron (at LS) to jump. Would that be considered instantaneous? Even if the speed of the jump occurred a million times slower, it would still be to the minus 15 sec. (if my math is right ) ---Still fast.

The other model could be of a tangentially based orbit of the electron (Gryziński M.)--of which, in this case, the electron, when, at 'some' time during its cycle (orbit, tangential or distal?), would lose the photon. The crossing point to another shell could very easily be at the tangential proximity to the nucleus with a much shorter distance to make the 'jump'. In this case, the 'jump' may be of even a less time difference than the first scenario (even more instantaneous).

Anyone have any other thoughts?---(I hope that this post isn't considered overly-speculative.)

 

[rewebster]

Well, I don't think either scenario is correct.


I think that both imply the speed, at least, which the 'jump' could occur.

 

[rewebster]

Does the electron disappear?

As for the topic of the thread itself--IMHO--no --I would say that it reacts so quickly that present day measuring devices just can't record the transition.







And as to 'reflection' of a photon, I guess I'll have to keep to my own hypothesis of what happens --(which I can't post here for several reasons--one, it being VERY over-speculative; and, two, there are still a few loose ends to the whole)

 

[reilly]

Of course we can consider a gazillion particles. Both in classical and quantum physics, we can replace the motion of the gazillion particles by the motion of the center of mass -- that's how we obtain planetary and lunar orbits. So. to a first approximation, the QM of the moon can be safely described by the QM of a point particle of moon mass M -- one could go a next step, and consider the moon to be made of the gazillion particles in a potential well roughly the size of the moon. For the first approximation, standard tunneling will show that the probability of the moon to tunnel through almost any potential barrier is of the order (guesswork) 10**-(100)(an estimate of the transmission coefficient. )For the second approximation, the WKB method should work nicely -- a good homework problem. (A great irony: one of the best discussions of tunneling, including the WKB method, can be found in Bohm's QM book.)

Once again, I agree with vanesch (Post 14).
Regards,
Reilly Atkinson

 

[reilly]

rewebster: Once again, this problem was worked to death in the 1930s. Time dependent perturbation theory does an excellent job of describing the dynamics of atomic jumps, cf, Weisskopf and Wigner, Breit and Wigner (after WWII) Go back, whether in Google, or such classics as Condon and Shortley -- Theory of Atomic Spectra, and, if I recall correctly, see also Blatt and Weisskopf's book Theoretical Nuclear Physics;, Schwinger's volume of key QED papers, Quantum Electrodynamics, Dirac's QM book, Books by Jauch and Rohrlich, Schweber -- his old text, and more recent history of QED -- Wentzel,, Akheiser and Berestski and on and on and on.

Everything you want to know about this issue can be found in the literature.

If you want to pursue what you write below, then your best bet is probably the WKB method, which ties together QM and classical mechanics. (And, don't forget the Dirac Eq. for hydrogen).

In QM, as we know it now, there really is no "jump", as there was in the old quantum theory of Bohr and Sommerfeld. That's why it's important to study the time dependence of the radiation process, which shows a smooth transition from one state to another -- for electrons and other charged particles, and photons as well.

Check out the literature. What you want to know has been there a long, long time.

Regards,
Reilly Atkinson

On my question in 51 and in relation to the electron 'jump':

What I was moving toward was two possibilities.

The first, taking one given radius of the hydrogen atom and hypothetically taking it as the distance between shells (I haven't found anything on the measured distances between shells) in a Copernican based model, the time may be around 5 x 10 to the minus 21 sec. for the electron (at LS) to jump. Would that be considered instantaneous? Even if the speed of the jump occurred a million times slower, it would still be to the minus 15 sec. (if my math is right ) ---Still fast.

The other model could be of a tangentially based orbit of the electron (Gryziński M.)--of which, in this case, the electron, when, at 'some' time during its cycle (orbit, tangential or distal?), would lose the photon. The crossing point to another shell could very easily be at the tangential proximity to the nucleus with a much shorter distance to make the 'jump'. In this case, the 'jump' may be of even a less time difference than the first scenario (even more instantaneous).

Anyone have any other thoughts?---(I hope that this post isn't considered overly-speculative.)

 

[Tyris]

The thing about the moon is, people are always looking at it. It contains so many entities, that it would take a few hundred years to decohere and become uncertain - but people keep observing it, and it collapses back to one state of being.