Electron Transitions and the Uncertainty Principle

[TheDestroyer]

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?

 

[DaveC426913]

The electron orbital does not define where the electron is, it defines where the electron will likely be when we go looking for it. When we find it, there it is. Quantum theory insists that we cannot know anything about it, and indeed, it is meaningless to ask, while we are not looking at it.

This is the crux of the weirdness that is QM. Scaled up, it means that the Moon does not necessarily exist when we are not looking at it.

 

[LnGrrrR]

Dave, wouldnt' an equally ridiculous interpretation of QM state that the Moon is anywhere in the sky within a certain range, and it just 'appears' in a certain spot when we look at it? :)

 

[chroot]

LnGrrrR:

No. The moon is not a quantum-mechanical object. It's a macroscopic object, subject to decoherence by many billions of interactions with other objects (photons, charged particles, etc.).

It's silly to expect a macroscopic object to behave quantum-mechanically.

- Warren

 

[LnGrrrR]

Chroot,

Read what Dave wrote ("scaled up") and I think you'll get where I'm coming from.

 

[chroot]

LnGrrrR:

I get where you're coming from. You want to equate the moon to an electron, and therefore ascribe the electron's behavior to the moon. Sorry, it ain't that easy. Dave's comment is pretty inaccurate.

- Warren

 

[LnGrrrR]

Chroot,

I think he was being facetious, as was I. :) I don't think either of us were being serious, just pointing out that our 'normal' mode of thinking doesn't really work for QM.

 

[ZapperZ]

Chroot,

I think he was being facetious, as was I. :) I don't think either of us were being serious, just pointing out that our 'normal' mode of thinking doesn't really work for QM.

You'd be surprise. Just look at the thread on the "tunneling" possibility of a tennis ball. People are arguing that it is possible! Yet, when I ask for evidence or theoretical derivation of such a thing, people point to me tunneling of electrons, as IF this is the same beast.

Whenever I see a discussion like this, my first inclination is to point to Phil Anderson's famous motto: MORE IS DIFFERENT! Just because an object is made up of a gazillion electrons, or atoms, doesn't mean that it is governed by the same rules as those individual electrons and atoms.

Read up on emergent properties, folks!

Zz.

 

[LnGrrrR]

Zapperz,

Yup...that's some sort of logical fallacy as well, though I can't remember the name of it. (For instance, no human can see atoms with the naked eye, and everything is made up of atoms...therefore, no one can see anything with the naked eye. :)

 

[DaTario]

LnGrrrR:

It's silly to expect a macroscopic object to behave quantum-mechanically.

- Warren

In a sentence like this one, it is important to mention what specific quantum property you are referring to, for otherwise its claim will be wrong, as the very existence of macroscopic objects is a quantum event.

Regarding the OP, the conclusion that the electron desappears would only be valid if, in a given instant t, the whole wave function of the electron vanish. The transient states between two stationary states (eigen functions of the Hamiltonian) are all non zero functions of amplitude of probability in space.

Unitarity of time evolution may be used in this discussion, too, in order to prove the preservation of the norm of rho(t) (density matrix).

Best Regards,

DaTario

 

[ZapperZ]

In a sentence like this one, it is important to mention what specific quantum property you are referring to, for otherwise its claim will be wrong, as the very existence of macroscopic objects is a quantum event.

Can you tell me what specific quantum property is relevant for something as large as the moon?

Zz.

 

[DaveC426913]

OK, I was being a bit sensationalist, and that is a disservice to the OP.

The Moon not being there is a concept - much like the idea that all the air in a room might suddenly gather in one corner.

These phenomena happen on the atomic scale, but the effect scales inversely to the number of atoms involved. An object of ANY macroscopic scale will take a time scale on the order of the age of the universe (or more - way more) to have this happen.

However, my point was that, in principle, the concept is valid. QM teaches us that the things we consider stable objects, the things we can count on - a chunk of rock sitting on the table is really a chunk of rock sitting on the table - are slipperier than we thought.

Nonetheless, withdrawn.

 

[vanesch]

However, my point was that, in principle, the concept is valid. QM teaches us that the things we consider stable objects, the things we can count on - a chunk of rock sitting on the table is really a chunk of rock sitting on the table - are slipperier than we thought.

Nonetheless, withdrawn.

Too bad you withdraw your statement :-)

There is a strange thing going on with quantum theory, and people are induced to say all kinds of weird things in order for the moon to be there!

If I say that the moon is there in 3-dim Euclidean space and is attracted by the earth, then everybody says "horray"...

If I say that the moon is tracing out a 4-volume on a spacetime manifold, of which we happen to observe a space-like slice, and is in fact following a geodesic on a 4-dim manifold, then everybody says "horray"...

But if I dare to say that the moon is described by a component of a vector in Hilbert space, then many people go saying "booh"!

Now, you'd think that those same people just think that quantum theory has limited validity. But if you ask them if quantum theory is a universally valid theory, then they say "yes".

 

[vanesch]

Can you tell me what specific quantum property is relevant for something as large as the moon?

Isn't this similar to asking what specific general relativity property is relevant for something as light and slow as the moon ? And to say that the moon is NOT something that ought to be described by general relativity, but by Newtonian gravity ?

Just for the sake of clarity: of course it is *ridiculous* to go use quantum theory, or general relativity, to describe something like the moon, because you make the practical problem way too hard, and Newtonian theory is by far adequate.

But I find it strange that people jump up and down when one wants to make the thought experiment of describing a macroscopic object using quantum theory - while they don't do that when one uses general relativity for a relatively light object.

 

[ZapperZ]

Isn't this similar to asking what specific general relativity property is relevant for something as light and slow as the moon ? And to say that the moon is NOT something that ought to be described by general relativity, but by Newtonian gravity ?

No, it is not similar, because they both converge at some scale.

I haven't seen QM properties being formulated to include a gazillion particles and converge to form the behavior of a moon.

Have you?

Zz.

 

[vanesch]

I haven't seen QM properties being formulated to include a gazillion particles and converge to form the behavior of a moon.

Isn't this essentially what decoherence theory tries to do ? To derive the appearance of a classical world in complex enough quantum interactions ?
Now, it is of course easier to establish the relationship between the GR and Newtonian case, because in both cases, the point-particle approximation is made and we deal only with a few degrees of freedom (accepting this approximation of saying that the moon is a point particle!). So the calculations can be done more explicitly.
Nevertheless, I appreciate Zeh and Co's approach in decoherence to arrive - in most cases - at rather classical situations. But again, the "demonstrations" are much rougher, because of the number of degrees of freedom involved. Nevertheless, I find this sufficiently encouraging to believe that the basic tenet of the decoherence programme is correct and to understand, from that, that Newtonian physics is a good approximation to the quantum solution in this case.

 

[ZapperZ]

Too bad you withdraw your statement :-)

There is a strange thing going on with quantum theory, and people are induced to say all kinds of weird things in order for the moon to be there!

If I say that the moon is there in 3-dim Euclidean space and is attracted by the earth, then everybody says "horray"...

If I say that the moon is tracing out a 4-volume on a spacetime manifold, of which we happen to observe a space-like slice, and is in fact following a geodesic on a 4-dim manifold, then everybody says "horray"...

But if I dare to say that the moon is described by a component of a vector in Hilbert space, then many people go saying "booh"!

Now, you'd think that those same people just think that quantum theory has limited validity. But if you ask them if quantum theory is a universally valid theory, then they say "yes".

I think you are twisting the issue here.

Many-body physics IS quantum mechanics, but being applied at a large number scale. I am NOT arguing this and you should know better than that.

But the theoretical convergence of SR/GR with classical Newtonian physics is something we do not have with QM and classical physics. I can set v<<c and I get convergence to Newtonian physics from SR in all aspect of mechanics. Do you see this in QM? Can I set n=LARGE and get ALL the classical dynamics of a tennis ball, dispite the so-called convergence in quantum SHO?

Since we care so much about the theoretical argument here, then let's consider this. There is this 50,000 lbs ugly cow sitting right in front of everyone that is being ignored here. There is STILL zero ability to "see" such emergent phenomena when you write down, with all your ability and expertise, the Hamitonian incorporating all the microscopic detail of the interactions. No matter how much you argue, that still hasn't changed. It is why superconductivity was not predicted, and it is why fractional quantum hall effect was not predicted. They are simply not there to be found. And as far as I know, NONE of the currely-accepted emergent phenomena were ever predicted out of such microscopic reductionist approach. Zilch! This is a huge ugly cow. Until someone can get this ugly cow to disappear, I see no convincing evidence to assume the contrary.

Zz.

 

[ZapperZ]

Isn't this essentially what decoherence theory tries to do ? To derive the appearance of a classical world in complex enough quantum interactions ?

But note what "decoherence" is. It isn't the study of ONE particle interacting with a gazillion external degree of freedom. It is the study of a many-body system being systematically "induced" into a classically random interaction! Example: interaction with a heat bath!

So already you assume you know how to handle the emergent property of a large number of particles into a simple form, and THEN, make that system interact with an external classically induced interaction. Don't you see how many levels of ad hoc stuff are introduced here? I can put stuff in by hand easily to account for many things. Is this what is necessary to be convincing?

Zz.

 

[Physics Monkey]

I think you are twisting the issue here.

Many-body physics IS quantum mechanics, but being applied at a large number scale. I am NOT arguing this and you should know better than that.

But the theoretical convergence of SR/GR with classical Newtonian physics is something we do not have with QM and classical physics. I can set v<<c and I get convergence to Newtonian physics from SR in all aspect of mechanics. Do you see this in QM? Can I set n=LARGE and get ALL the classical dynamics of a tennis ball, dispite the so-called convergence in quantum SHO?

Since we care so much about the theoretical argument here, then let's consider this. There is this 50,000 lbs ugly cow sitting right in front of everyone that is being ignored here. There is STILL zero ability to "see" such emergent phenomena when you write down, with all your ability and expertise, the Hamitonian incorporating all the microscopic detail of the interactions. No matter how much you argue, that still hasn't changed. It is why superconductivity was not predicted, and it is why fractional quantum hall effect was not predicted. They are simply not there to be found. And as far as I know, NONE of the currely-accepted emergent phenomena were ever predicted out of such microscopic reductionist approach. Zilch! This is a huge ugly cow. Until someone can get this ugly cow to disappear, I see no convincing evidence to assume the contrary.

Zz.

I'm not sure what you mean here, ZapperZ. These phenomenon certainly weren't predicted, but that doesn't mean that they aren't contained in a microscopic Hamiltonian. It simply means we weren't clever enough to see it with our crude methods of analysis. The same is true of QCD, for example, where we have this stunningly beautiful Lagrangian that contains so much rich physics which is nevertheless hidden from simple view by the complexity of the problem. I could see someone arguing that very little is to be gained, at the present time, by examing these complicated many body states from first principles, but I do think it is possible in principle. Do you agree?

 

[ZapperZ]

I'm not sure what you mean here, ZapperZ. These phenomenon certainly weren't predicted, but that doesn't mean that they aren't contained in a microscopic Hamiltonian. It simply means we weren't clever enough to see it with our crude methods of analysis. The same is true of QCD, for example, where we have this stunningly beautiful Lagrangian that contains so much rich physics which is nevertheless hidden from simple view by the complexity of the problem. I could see someone arguing that very little is to be gained, at the present time, by examing these complicated many body states from first principles, but I do think it is possible in principle. Do you agree?

Actually, I don't.

The Hamiltonian for superconductivity and fractional Hall effect starts off with a many-body ground state. In BCS-theory, for example, you already start off with a Fermi-Liquid state that has renormalized all of the weak-coupling electron-electron interaction into a many one-body problem. This is not the "microscopic Hamiltonian".

In case you didn't read Laughlin's Nobel Prize speech, he assigned this to his students in a graduate quantum class, i.e. starting from the microscopic interaction at the individual particles and then try to "derive" superconductivity. It can't be done. It was a trick question.

Zz.

 

[vanesch]

In case you didn't read Laughlin's Nobel Prize speech, he assigned this to his students in a graduate quantum class, i.e. starting from the microscopic interaction at the individual particles and then try to "derive" superconductivity. It can't be done. It was a trick question.

Yes, but so was Fermat's last theorem for a few centuries... people tried and couldn't prove it.
We've been over this already a few times now and it is clear that we have different opinions on the subject. My main problem with your view, however, is that I don't really understand it.

I'm not disputing that it isn't wise, or practical, to build directly phenomenological models. For sure it is.
I'm not even disputing that certain emergent phenomena are probably so deeply burried into the microscopic interactions, that you can even bet on it that no-one in any forseeable future will find the right analysis to show them to you with some rigor.

However, the point I've been repeating is that to CLAIM that this is impossible in principle has no foundation - just as well as the claim that it MUST be possible, btw. There must be hidden, in the platonic mathematical world, a proof that the emergent phenomenon DOES follow from the microscopic prescription, OR a proof that the emergent phenomenon DOES NOT follow from that microscopic prescription, OR a mathematical issue such as a singularity or something that prevents you from obtaining the solution.
In the first case (which I, as all reductionists, conjecture), well, Laughlin is wrong ; in the second case, well, Laughlin is right, and reductionists take it that there is then an ERROR in the microscopic physics, and in the third case, Laughlin is right and reductionists say that the microscopic specification is INCOMPLETE.
There are cases where we are in the first case (and this has been explicitly demonstrated) ; a simple example is of course the kinetic theory of gasses. I'm not aware of EXPLICIT PROOFS of the second and third cases. I'm aware - as you point out - of failed attempts of the first case ; but to me that's like people failing to find the proof of Fermat's last theorem: it's not because you don't find the proof that the theorem is false.

Now, I leave open the possibilities of 2 and 3 (although they'd shock me!) ; but you should leave open the possibility of 1 too . After all, we don't have any proof one way or another, so it is just a matter of personal opinion.

 

[vanesch]

... in the third case, Laughlin is right and reductionists say that the microscopic specification is INCOMPLETE.

To continue, I would take it that *this* is the non-reductionist POV, no ? That the microscopic specification is incomplete and that you DO RUN into troubles, mathematically, in principle, if you try to derive the emergent phenomenon from the micro laws (that you can prove that you do run in a singularity, or an indetermined case or something). But my point is that you cannot claim that without a proof - in as much a way as that you cannot claim that the phenomenon IS derivable, without a proof.

So at the very best, this is an open question. There is NO proof, either way or another, that the microscopic prescription contains in its axiomatic system and what is in principle derivable from it, the emergent phenomenon or not. We are in the same situation as, say, 50 years ago, when there was no proof of Fermat's last theorem, and no proof (for instance, by counter example) of its falsity. So one could not claim that Fermat's last theorem was true, but one could not claim that it was false either.

I, personally, have the profound conviction that reductionism must be true (as described by Weinberg) - what doesn't mean that our *current* theories must be true. What I mean by that is that, IF it turns out that we are in case 2 or 3, then I consider that there is a problem on a fundamental level with the theory. And this is where I think that there is a danger in accepting permaturely a rejection of reductionism as a principle: we might be too easy-going on fundamental problems. Each time that there might be an indication that the microphysics might NOT predict a macroscopic phenomenon, we might conclude that, well, that's only a problem for reductionists - no big deal... while it might be our best indication of something fishy down under.
Nevertheless, I admit that this is just personal opinion - but so it the opposite view !

 

[Physics Monkey]

Hi ZapperZ,

Vanesch has already made a nice response which includes most of what I would have mentioned.

Thanks for reminding me about about Laughlin's Nobel Prize lecture. I have read it, and I recall now that the comment about superfluidity confused me greatly. You see my background is in BEC physics, and in BEC physics it is possible to start from a microscopic picture and go all the way to superfluidity by (I would argue) a controlled and well understood route.

If Laughlin is saying that it is often not useful/productive/insightful to stare at a microscopic Hamiltonian, I can certainly strongly agree. Laughlin's wavefunction, like the elegant Cooper ansatz, captured beautifully the relevant physics in a way we can understand. I don't think that insight came from staring at any microscopic interaction. However, if he is saying that the microscopic Hamiltonian doesn't contain all the physics, I respectfully disagree. Is that what he is saying, in your opinion? Better yet, is that what you think? If so, I am curious to understand where or how you suppose the crossover to take place. When does the microscopic Hamiltonian stop working?

 

[ZapperZ]

Hi ZapperZ,

Vanesch has already made a nice response which includes most of what I would have mentioned.

Thanks for reminding me about about Laughlin's Nobel Prize lecture. I have read it, and I recall now that the comment about superfluidity confused me greatly. You see my background is in BEC physics, and in BEC physics it is possible to start from a microscopic picture and go all the way to superfluidity by (I would argue) a controlled and well understood route.

If Laughlin is saying that it is often not useful/productive/insightful to stare at a microscopic Hamiltonian, I can certainly strongly agree. Laughlin's wavefunction, like the elegant Cooper ansatz, captured beautifully the relevant physics in a way we can understand. I don't think that insight came from staring at any microscopic interaction. However, if he is saying that the microscopic Hamiltonian doesn't contain all the physics, I respectfully disagree. Is that what he is saying, in your opinion? Better yet, is that what you think? If so, I am curious to understand where or how you suppose the crossover to take place. When does the microscopic Hamiltonian stop working?

I believe he is saying that the microscopic Hamiltonian does tell you where so-and-so is. I don't think he can (nor can anyone else, even Weinberg) say that it is inherently isn't in there, even though in many instances, he does seems to appear to hold that ground.

Being pragmatic, my view has always been "if it doesn't do you any good, why are we bothering with it" type of philosophy. As I have said waaaaay before, and as vanesch has pointed out, we have no way of testing if our accurate microscopic "fundamental" description is complete to be able to account for the large scale collective phenomena. If we can, many-body physics would not be the "First Principle" starting point for such things. And I can't say where, if there is an inherent incompleteness, where such crossover is. Mesoscopic physics is still an unfamiliar field of study, at least to me.

And besides, is just a simple crossover, or is it actually a "phase transition" where you actually have a discontinuity, rendering your extrapolation invalid? Till we find out, I would say it is premature to deduce what can be done. All I know is that right now, there are no microscopic theoretical description that can do such extrapolation.

Zz.

 

[masudr]

Very interesting. So ZapperZ, do you think in principle, the emergent phenomena could not be predicted from basic fundamental principles, assuming we had a super-powerful computer, say a universal Turing machine with infinite tape?

In fact let me slightly re-phrase my question. If we had a one super-complete self-contained theory that was capable of describing every known interaction, and we had at our hands the most powerful supercomputer, could we then work out probabilities and describe emergent macroscopic results?

Or do you think that either:

(a) such a complete theory is impossible;
(b) the above is possible but the emergent phenomena could not be described using our fundamental theories;
(c) even if the above two are possible, since the super-machine is actually physically impossible, we will never be able to do the required calculations?

In fact, I address these questions not just to ZapperZ, but to all concerned.

EDIT: Personally, I'm a part-reductionist (so I believe that a single fundamental framework to describe all known interactions is possible) but am certain that most macroscopic phenomena will never be derived from a more fundamental set of principles. 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. In principle, however, this doesn't mean that the emergent phenomena cannot arise from the more fundamental principles, it just means that we won't be able to prove that it is so. I believe that numerical calculations can still be done, but that we will probably never have the computational power (even theoretically) to do these calculations. So that sets my answer as (c).

 

[LnGrrrR]

Masudr,

Given what I currently know of QM (and granted, that's not much!) I would say that it would be option A, only because which direction a particle will go in seems to be completely unknowable.

A question for my own knowledge...once a photon is measured, can someone trace its entire path from the plate to the light source?

 

[masudr]

Well, the point is that one wouldn't necessarily calculate the worldlines of every particle, but probably the state vector, or something else (whatever else the new theory would say is fundamental).

Note that nowhere did I imply that we would have the motion of every particle.

 

[LnGrrrR]

Masudr,

No, I meant, in an experiment today, can we 'trace back' the path of a measured photon after it hits the plate? I'm thinking we can't, but I'd like to know for sure. :)

 

[ZapperZ]

Very interesting. So ZapperZ, do you think in principle, the emergent phenomena could not be predicted from basic fundamental principles, assuming we had a super-powerful computer, say a universal Turing machine with infinite tape?

In fact let me slightly re-phrase my question. If we had a one super-complete self-contained theory that was capable of describing every known interaction, and we had at our hands the most powerful supercomputer, could we then work out probabilities and describe emergent macroscopic results?

Or do you think that either:

(a) such a complete theory is impossible;
(b) the above is possible but the emergent phenomena could not be described using our fundamental theories;
(c) even if the above two are possible, since the super-machine is actually physically impossible, we will never be able to do the required calculations?

In fact, I address these questions not just to ZapperZ, but to all concerned.

EDIT: Personally, I'm a part-reductionist (so I believe that a single fundamental framework to describe all known interactions is possible) but am certain that most macroscopic phenomena will never be derived from a more fundamental set of principles. 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. In principle, however, this doesn't mean that the emergent phenomena cannot arise from the more fundamental principles, it just means that we won't be able to prove that it is so. I believe that numerical calculations can still be done, but that we will probably never have the computational power (even theoretically) to do these calculations. So that sets my answer as (c).

Honestly, I don't know. But I think this is a moot question since if we have such ability, we won't be talking about it.

But here's what we do know:

1. The microscopic Hamiltonian that we CAN write doesn't produce or tell us anything about emergent phenomena at the large scale.

2. That at some point, such collective behavior can produce something EXTREMELY strange in which the SMALLEST available "unit" is smaller than what we think are the fundamental constituent. I'm talking about fractional charge and fractional quantum hall effect. How does one get 1/5 e as the smallest amount of charge that can pass through a constriction when the smallest individual particle that make up the conglomerate is 1e?

While I cannot conclusively provide the necessary "proof" of the boundary between those two scales, I can still point out the emergent behavior that simply defy the ability for the microscopic description that we can currently write to describe. Whether some people find these convincing is a different matter. Those are the observations.

Zz.

 

[vanesch]

EDIT: Personally, I'm a part-reductionist (so I believe that a single fundamental framework to describe all known interactions is possible) but am certain that most macroscopic phenomena will never be derived from a more fundamental set of principles. 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.

You're thinking along the lines of Goedel's theorem ? But let us not forget that macroscopic properties do not correspond to randomly selected syntactically correct formal statements; they are drawn from a much smaller set of statements, for which there DO exist kinds of "existence proofs".

I'm maybe naive, but: the 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). The hamiltonian should also exist, as a sum of 2-system interaction hamiltonians. A very big sum for sure, but a finite sum of self-adjoint operators. Now a finite sum of self-adjoint operators is, I think, a self-adjoint operator, no ?
Now I also think that its exponentiation exists, and gives rise to a unitary operator, U(t). I'm not sure it exists for all t, but I think so:
If H is a self-adjoint operator, doesn't exp(- I t H) exist as a unitary operator ?

Once we have a unitary operator U(t), we're now stuck with the "macroscopic property". That shouldn't be too difficult, though: the experiment establishing a macroscopic property has only a finite set of different outcomes, so this corresponds to slicing up the hilbert space as a finite sum of orthogonal eigenspaces, from which the measurement operator A of the test of the macroscopic property can be found.

We now seem to have a self-adjoint hamiltonian, a measurement operator A, and a time evolution operator U(t). I don't see where we should hit *fundamental* mathematical difficulties which could be forward in a non-existence-of-solution kind of proof.

Classical physics is nastier in this respect, because the flow on phase space doesn't guarantee the existence of flow lines for all of t in many cases - so it is harder to be sure that a classical solution for all of t exists, than in the quantum case, no ?

 

[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-------